{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0001","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c6b36ba6964322ff5f9d790b2054769bc7a6c314d3660f2a5ba890b1d94c5589","family_id":"qf-congruence-labeled-sss","seed":202610075001,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"1\",\"5\",\"4\"],[\"1\",\"5\",\"4\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(1, 0), A3=(1, 2) and B1=(3, 5), B2=(4, 5), B3=(4, 3), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"Yes","explanation":"In the fixed order 12,13,23, squared sides are A=[1, 5, 4] and B=[1, 5, 4]. Compare all three to obtain Yes. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0002","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f6c228bc211fc4c76038f0d43cd4b23392ca8555c2cc925dd40e80fcf0fba049","family_id":"qf-congruence-labeled-sss","seed":202610075002,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"4\",\"10\",\"10\"],[\"9\",\"10\",\"13\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(2, 0), A3=(1, 3) and B1=(0, 0), B2=(3, 0), B3=(1, 3), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[4, 10, 10] and B=[9, 10, 13]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0003","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d7d10ffad8daebbf23217c6ab9f1d4f2cac9733c8df922cb50790cb8995e04bd","family_id":"qf-congruence-labeled-sss","seed":202610075003,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"9\",\"17\",\"20\"],[\"9\",\"26\",\"29\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 4) and B1=(0, 0), B2=(3, 0), B3=(1, 5), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[9, 17, 20] and B=[9, 26, 29]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0004","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b6b08c7ada0904fa80baef4103f2ebcb6aaf75e46e332c441d5e6200a9c7c4f6","family_id":"qf-congruence-labeled-sss","seed":202610075004,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"16\",\"26\",\"34\"],[\"16\",\"26\",\"50\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(4, 0), A3=(1, 5) and B1=(0, 0), B2=(4, 0), B3=(-1, 5), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[16, 26, 34] and B=[16, 26, 50]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0005","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3e7be9900c4827828f4e1782e0a29ee6d7052d7d3bbe0131553b6e943ba2b677","family_id":"qf-congruence-labeled-sss","seed":202610075005,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"25\",\"37\",\"52\"],[\"25\",\"37\",\"52\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(5, 0), A3=(1, 6) and B1=(3, 5), B2=(8, 5), B3=(4, -1), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"Yes","explanation":"In the fixed order 12,13,23, squared sides are A=[25, 37, 52] and B=[25, 37, 52]. Compare all three to obtain Yes. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0006","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ab48fd30699a0bef4aadf86243ac9d7166bd3006759f127e4bc447cc6c85f1d2","family_id":"qf-congruence-labeled-sss","seed":202610075006,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"36\",\"50\",\"74\"],[\"49\",\"50\",\"85\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(6, 0), A3=(1, 7) and B1=(0, 0), B2=(7, 0), B3=(1, 7), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[36, 50, 74] and B=[49, 50, 85]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0007","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1ebb0aaa939618b4f829fc753a5d1dd26bb283b54283b530c61822e37f26f4e9","family_id":"qf-congruence-labeled-sss","seed":202610075007,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"49\",\"65\",\"100\"],[\"49\",\"82\",\"117\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(7, 0), A3=(1, 8) and B1=(0, 0), B2=(7, 0), B3=(1, 9), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[49, 65, 100] and B=[49, 82, 117]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0008","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9236606ef128f6a661fe22bcb3cc62f9883ef33d58ca79bae0c1bed9b1baafab","family_id":"qf-congruence-labeled-sss","seed":202610075008,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"64\",\"82\",\"130\"],[\"64\",\"82\",\"162\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(8, 0), A3=(1, 9) and B1=(0, 0), B2=(8, 0), B3=(-1, 9), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[64, 82, 130] and B=[64, 82, 162]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0009","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b1637b190d64efc6e64792292152bd934068ed3909d2a1b18a0b6868d5b785fd","family_id":"qf-congruence-labeled-sss","seed":202610075009,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"81\",\"101\",\"164\"],[\"81\",\"101\",\"164\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(9, 0), A3=(1, 10) and B1=(3, 5), B2=(12, 5), B3=(4, -5), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"Yes","explanation":"In the fixed order 12,13,23, squared sides are A=[81, 101, 164] and B=[81, 101, 164]. Compare all three to obtain Yes. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0010","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e4237e831b40756701d0fc878638bf56d825c9712b0aa7d568fddb3b004769df","family_id":"qf-congruence-labeled-sss","seed":202610075010,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"100\",\"122\",\"202\"],[\"121\",\"122\",\"221\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(10, 0), A3=(1, 11) and B1=(0, 0), B2=(11, 0), B3=(1, 11), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[100, 122, 202] and B=[121, 122, 221]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0011","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"75562930f2163b79e1417b4c4c2cc08bb1c5e6bd6ec3aafe7a056dcb761af67a","family_id":"qf-congruence-labeled-sss","seed":202610075011,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"121\",\"145\",\"244\"],[\"121\",\"170\",\"269\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(11, 0), A3=(1, 12) and B1=(0, 0), B2=(11, 0), B3=(1, 13), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[121, 145, 244] and B=[121, 170, 269]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0012","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d665b6e7590bfe4da16b82a267df57dd8945eec3aee06fa7ecf215e1ae2c87c5","family_id":"qf-congruence-labeled-sss","seed":202610075012,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"144\",\"170\",\"290\"],[\"144\",\"170\",\"338\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(12, 0), A3=(1, 13) and B1=(0, 0), B2=(12, 0), B3=(-1, 13), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[144, 170, 290] and B=[144, 170, 338]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0013","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9ee93c21b566fffcfa12d4ef8fc8a21f5747f32f63f08556982272dce8071bbb","family_id":"qf-congruence-labeled-sss","seed":202610075013,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"169\",\"197\",\"340\"],[\"169\",\"197\",\"340\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(13, 0), A3=(1, 14) and B1=(3, 5), B2=(16, 5), B3=(4, -9), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"Yes","explanation":"In the fixed order 12,13,23, squared sides are A=[169, 197, 340] and B=[169, 197, 340]. Compare all three to obtain Yes. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0014","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9640196832b1fa9394fd72cbaf29bc61d73048270404c8f7077b35a0b038e9d8","family_id":"qf-congruence-labeled-sss","seed":202610075014,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"196\",\"226\",\"394\"],[\"225\",\"226\",\"421\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(14, 0), A3=(1, 15) and B1=(0, 0), B2=(15, 0), B3=(1, 15), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[196, 226, 394] and B=[225, 226, 421]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0015","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e75f9d58d60571421546d64a6ee27a663dcb6dd23b999c55a5a8de19f0515a69","family_id":"qf-congruence-labeled-sss","seed":202610075015,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"225\",\"257\",\"452\"],[\"225\",\"290\",\"485\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(15, 0), A3=(1, 16) and B1=(0, 0), B2=(15, 0), B3=(1, 17), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[225, 257, 452] and B=[225, 290, 485]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0016","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"01b2a27f74041f7b205495188c27feb900d8ebb26eeb9012d3a065ed00d9700f","family_id":"qf-congruence-labeled-sss","seed":202610075016,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"256\",\"290\",\"514\"],[\"256\",\"290\",\"578\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(16, 0), A3=(1, 17) and B1=(0, 0), B2=(16, 0), B3=(-1, 17), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[256, 290, 514] and B=[256, 290, 578]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0017","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0eeab7c214c9894f923bffb4f52cccf133a35d7aff78f70a4ade0db1b225eba4","family_id":"qf-congruence-labeled-sss","seed":202610075017,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"289\",\"325\",\"580\"],[\"289\",\"325\",\"580\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(17, 0), A3=(1, 18) and B1=(3, 5), B2=(20, 5), B3=(4, -13), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"Yes","explanation":"In the fixed order 12,13,23, squared sides are A=[289, 325, 580] and B=[289, 325, 580]. Compare all three to obtain Yes. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0018","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"02be751ce0af9d9e8ac5de46f50deae6a3bd77a059683dfe14853133d89d2b41","family_id":"qf-congruence-labeled-sss","seed":202610075018,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"324\",\"362\",\"650\"],[\"361\",\"362\",\"685\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(18, 0), A3=(1, 19) and B1=(0, 0), B2=(19, 0), B3=(1, 19), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[324, 362, 650] and B=[361, 362, 685]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0019","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d570b292835c316c99246e96d3fc476d5fd6aa951f891ec3bf5ee322a113df2b","family_id":"qf-congruence-labeled-sss","seed":202610075019,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"361\",\"401\",\"724\"],[\"361\",\"442\",\"765\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(19, 0), A3=(1, 20) and B1=(0, 0), B2=(19, 0), B3=(1, 21), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[361, 401, 724] and B=[361, 442, 765]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0020","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6470474b1310abfe59b3512f6dfb4d37e25191e2d0e6587ed47367ad40aca5ab","family_id":"qf-congruence-labeled-sss","seed":202610075020,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"400\",\"442\",\"802\"],[\"400\",\"442\",\"882\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(20, 0), A3=(1, 21) and B1=(0, 0), B2=(20, 0), B3=(-1, 21), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[400, 442, 802] and B=[400, 442, 882]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0021","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4222ec1518ef7107cf05a972b66cd4257f551feaac38025ca9cd8799abbea788","family_id":"qf-congruence-labeled-sss","seed":202610075021,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"441\",\"485\",\"884\"],[\"441\",\"485\",\"884\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(21, 0), A3=(1, 22) and B1=(3, 5), B2=(24, 5), B3=(4, -17), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"Yes","explanation":"In the fixed order 12,13,23, squared sides are A=[441, 485, 884] and B=[441, 485, 884]. Compare all three to obtain Yes. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0022","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"92636be8ca9bf2716649bbda46aaab1749dbc5f6947373745770e3ebc5244fe9","family_id":"qf-congruence-labeled-sss","seed":202610075022,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"484\",\"530\",\"970\"],[\"529\",\"530\",\"1013\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(22, 0), A3=(1, 23) and B1=(0, 0), B2=(23, 0), B3=(1, 23), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[484, 530, 970] and B=[529, 530, 1013]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0023","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0fb1c406bc03a82c069409d9f8d4b84b834147474806925411cae1d536142ea2","family_id":"qf-congruence-labeled-sss","seed":202610075023,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"529\",\"577\",\"1060\"],[\"529\",\"626\",\"1109\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(23, 0), A3=(1, 24) and B1=(0, 0), B2=(23, 0), B3=(1, 25), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[529, 577, 1060] and B=[529, 626, 1109]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0024","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cc0435c8b86b68b102c251044b224fa01c1bdb783b1f3aa17d7c48299de720e6","family_id":"qf-congruence-labeled-sss","seed":202610075024,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"576\",\"626\",\"1154\"],[\"576\",\"626\",\"1250\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(24, 0), A3=(1, 25) and B1=(0, 0), B2=(24, 0), B3=(-1, 25), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"No","explanation":"In the fixed order 12,13,23, squared sides are A=[576, 626, 1154] and B=[576, 626, 1250]. Compare all three to obtain No. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0025","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e276a705e6e21bb845c0417e87a472e32867b869620a2b47fdd8b56e7025bc68","family_id":"qf-congruence-labeled-sss","seed":202610075025,"semantic_template":"qf-congruence-labeled-sss/{\"inputs\":[[\"625\",\"677\",\"1252\"],[\"625\",\"677\",\"1252\"]],\"operation\":\"labeled_sss\"}"},"fields":{"title":"SSS Congruence with Fixed Vertex Labels","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(25, 0), A3=(1, 26) and B1=(3, 5), B2=(28, 5), B3=(4, -21), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Do all three corresponding sides satisfy labeled SSS congruence?","answer":{"kind":"short_text","value":"Yes","explanation":"In the fixed order 12,13,23, squared sides are A=[625, 677, 1252] and B=[625, 677, 1252]. Compare all three to obtain Yes. Reflection is allowed; failure of this correspondence does not reject every other vertex permutation."},"skills":["SSS Congruence with Fixed Vertex Labels"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0026","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"395c0a082f82ed17b973d3ff2c2554a35c2b8d83bff1b40be14eaa1a6f6a4d03","family_id":"qf-congruence-corresponding-squared-side","seed":202610075026,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"0\",\"1\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(0, 1), A3=(-1, 0) and B1=(3, 5), B2=(3, 4), B3=(2, 5), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"1","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 1. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0027","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"13596ff180b609468733e5bac7ae4033408230bb215612ef1a9f31b6a267beed","family_id":"qf-congruence-corresponding-squared-side","seed":202610075027,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"1\",\"2\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(1, 2), A3=(-2, 1) and B1=(3, 5), B2=(4, 3), B3=(1, 4), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"5","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 5. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0028","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e0d098a0a3ca8043b632edde93389dee3c7d4895d4b11f9357ac9fba73e11cb9","family_id":"qf-congruence-corresponding-squared-side","seed":202610075028,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"2\",\"3\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(2, 3), A3=(-3, 2) and B1=(3, 5), B2=(5, 2), B3=(0, 3), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"13","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 13. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0029","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"529489b01773ae457a73ecd0a4373a0c67cd1edb46f52a2f979276eff2f4f589","family_id":"qf-congruence-corresponding-squared-side","seed":202610075029,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"3\",\"4\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 4), A3=(-4, 3) and B1=(3, 5), B2=(6, 1), B3=(-1, 2), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"25","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 25. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0030","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"454cd3df1808d18ec6e75dce4c863a7aa3da856ca6dad2fb3045189b969a9393","family_id":"qf-congruence-corresponding-squared-side","seed":202610075030,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"4\",\"5\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(4, 5), A3=(-5, 4) and B1=(3, 5), B2=(7, 0), B3=(-2, 1), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"41","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 41. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0031","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ca8477d92d2c8297734e5c69cb445cebda51f3ff94ef11c257e4a915801b3971","family_id":"qf-congruence-corresponding-squared-side","seed":202610075031,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"5\",\"6\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(5, 6), A3=(-6, 5) and B1=(3, 5), B2=(8, -1), B3=(-3, 0), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"61","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 61. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0032","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0ca0041b478b541c6b939b520addb728cf0e5666c4c6516c4acc4c34994428dd","family_id":"qf-congruence-corresponding-squared-side","seed":202610075032,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"6\",\"7\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(6, 7), A3=(-7, 6) and B1=(3, 5), B2=(9, -2), B3=(-4, -1), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"85","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 85. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0033","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f14a154798e4b73995a1f18f556adcdc7aac34fbb53bf5d731b5c9ef213efd15","family_id":"qf-congruence-corresponding-squared-side","seed":202610075033,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"7\",\"8\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(7, 8), A3=(-8, 7) and B1=(3, 5), B2=(10, -3), B3=(-5, -2), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"113","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 113. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0034","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"70e002558d4200d83b1856d37e2920b8381e4506bcd2ae146c07c62371dc9b96","family_id":"qf-congruence-corresponding-squared-side","seed":202610075034,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"8\",\"9\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(8, 9), A3=(-9, 8) and B1=(3, 5), B2=(11, -4), B3=(-6, -3), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"145","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 145. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0035","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e59c479f7f3d752ee8132179970717da0f70ca078d8c15a89ab76359031ad820","family_id":"qf-congruence-corresponding-squared-side","seed":202610075035,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"9\",\"10\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(9, 10), A3=(-10, 9) and B1=(3, 5), B2=(12, -5), B3=(-7, -4), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"181","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 181. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0036","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"60966fde9074fb869e5d8a6c09a376f673fa21546dd13e82687230b7d1be3450","family_id":"qf-congruence-corresponding-squared-side","seed":202610075036,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"10\",\"11\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(10, 11), A3=(-11, 10) and B1=(3, 5), B2=(13, -6), B3=(-8, -5), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"221","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 221. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0037","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"38e2dfa0a581f3d8dbadecceda2923ee0294d174f557cd18d07504b5966ce2e8","family_id":"qf-congruence-corresponding-squared-side","seed":202610075037,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"11\",\"12\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(11, 12), A3=(-12, 11) and B1=(3, 5), B2=(14, -7), B3=(-9, -6), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"265","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 265. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0038","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eca5aac688baaf85bd826fa1634464a7e60439a9bd97e71ac004afa21e811a54","family_id":"qf-congruence-corresponding-squared-side","seed":202610075038,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"12\",\"13\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(12, 13), A3=(-13, 12) and B1=(3, 5), B2=(15, -8), B3=(-10, -7), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"313","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 313. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0039","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"71c45a76d7275bda3da4dc2494dfdd0e90691c1f54f0ca1ea18885ff72c2b354","family_id":"qf-congruence-corresponding-squared-side","seed":202610075039,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"13\",\"14\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(13, 14), A3=(-14, 13) and B1=(3, 5), B2=(16, -9), B3=(-11, -8), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"365","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 365. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0040","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7092c8e1a20c1412ff91057df34017aa8e385dd0a20f36a7533bcf9eb683ba76","family_id":"qf-congruence-corresponding-squared-side","seed":202610075040,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"14\",\"15\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(14, 15), A3=(-15, 14) and B1=(3, 5), B2=(17, -10), B3=(-12, -9), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"421","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 421. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0041","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4da10a6bce29a5587075f2ec4a848b35987c4637fb621676d8663ce7cac9d7b8","family_id":"qf-congruence-corresponding-squared-side","seed":202610075041,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"15\",\"16\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(15, 16), A3=(-16, 15) and B1=(3, 5), B2=(18, -11), B3=(-13, -10), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"481","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 481. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0042","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"abe967c3195023176bb390f37532552f638af1467e5c8b121040aeabc86c345e","family_id":"qf-congruence-corresponding-squared-side","seed":202610075042,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"16\",\"17\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(16, 17), A3=(-17, 16) and B1=(3, 5), B2=(19, -12), B3=(-14, -11), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"545","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 545. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0043","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"87615e8e3e2e18c240a86a262747daf8274d1d7f1c2bc65614816fbf59d38daa","family_id":"qf-congruence-corresponding-squared-side","seed":202610075043,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"17\",\"18\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(17, 18), A3=(-18, 17) and B1=(3, 5), B2=(20, -13), B3=(-15, -12), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"613","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 613. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0044","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d85364f4990792e8b41da865d9d74cd7c8689b323e43e7857e89155a6a33a745","family_id":"qf-congruence-corresponding-squared-side","seed":202610075044,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"18\",\"19\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(18, 19), A3=(-19, 18) and B1=(3, 5), B2=(21, -14), B3=(-16, -13), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"685","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 685. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0045","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cc6f3a09fb8e5cf2b58d33e043293e19c0707f3c96b474a10870fd80f46ccc44","family_id":"qf-congruence-corresponding-squared-side","seed":202610075045,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"19\",\"20\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(19, 20), A3=(-20, 19) and B1=(3, 5), B2=(22, -15), B3=(-17, -14), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"761","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 761. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0046","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6d87ecd6f671d85644964d53ff8c0c6057f6bf8a17b47ac7cb2ad0cf3e929a65","family_id":"qf-congruence-corresponding-squared-side","seed":202610075046,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"20\",\"21\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(20, 21), A3=(-21, 20) and B1=(3, 5), B2=(23, -16), B3=(-18, -15), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"841","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 841. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0047","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2c0fb4d68907ecef0dcd4af98c4e7ccd3e563093c12512d69e618df92ae6d0c6","family_id":"qf-congruence-corresponding-squared-side","seed":202610075047,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"21\",\"22\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(21, 22), A3=(-22, 21) and B1=(3, 5), B2=(24, -17), B3=(-19, -16), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"925","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 925. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0048","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7392ec7f9b54df006695ed81ccf40324b01b1082f1dc3b9df87320a88da5cd1e","family_id":"qf-congruence-corresponding-squared-side","seed":202610075048,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"22\",\"23\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(22, 23), A3=(-23, 22) and B1=(3, 5), B2=(25, -18), B3=(-20, -17), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"1013","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 1013. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0049","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2903f20cd088117b3b0eebb4a6b1bdfdb48a4034b52e196b6650b899cbb2a6d0","family_id":"qf-congruence-corresponding-squared-side","seed":202610075049,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"23\",\"24\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(23, 24), A3=(-24, 23) and B1=(3, 5), B2=(26, -19), B3=(-21, -18), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"1105","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 1105. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0050","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7284174d3872deff0873bb75dd02cff96a8e4fa313d30a197deb3ecd0e8bd03e","family_id":"qf-congruence-corresponding-squared-side","seed":202610075050,"semantic_template":"qf-congruence-corresponding-squared-side/{\"inputs\":[\"24\",\"25\"],\"operation\":\"corresponding_squared_side\"}"},"fields":{"title":"Corresponding Squared Side in Congruent Triangles","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(24, 25), A3=(-25, 24) and B1=(3, 5), B2=(27, -20), B3=(-22, -19), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. Full three-side congruence has been confirmed. Find the common squared length of A1A2 and B1B2.","answer":{"kind":"short_text","value":"1201","explanation":"Read the specified side after the complete labeled-congruence check, obtaining 1201. Agreement of just one side alone would not establish congruence."},"skills":["Corresponding Squared Side in Congruent Triangles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0051","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5fe1a35f763998b6592978ea48e87240bc7986532ae255c76f87a60859ca2790","family_id":"qf-congruence-first-mismatch","seed":202610075051,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"1\",\"5\",\"4\"],[\"1\",\"5\",\"4\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(1, 0), A3=(1, 2) and B1=(3, 5), B2=(4, 5), B3=(4, 3), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"none","explanation":"The ordered squared sides are A=[1, 5, 4] and B=[1, 5, 4]. The first mismatch is none; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0052","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1c5a3e1752232805a8e2fd8de936557f740b9ce2ac577fa260359897bbc103f7","family_id":"qf-congruence-first-mismatch","seed":202610075052,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"4\",\"10\",\"10\"],[\"9\",\"10\",\"13\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(2, 0), A3=(1, 3) and B1=(0, 0), B2=(3, 0), B3=(1, 3), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"12","explanation":"The ordered squared sides are A=[4, 10, 10] and B=[9, 10, 13]. The first mismatch is 12; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0053","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a37ee71b1e11cdcf15e3e54ff42e74d1d2a7fd9ffe53836bc56c80ba9e0cf940","family_id":"qf-congruence-first-mismatch","seed":202610075053,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"9\",\"17\",\"20\"],[\"9\",\"26\",\"29\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 4) and B1=(0, 0), B2=(3, 0), B3=(1, 5), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"13","explanation":"The ordered squared sides are A=[9, 17, 20] and B=[9, 26, 29]. The first mismatch is 13; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0054","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9ec55a551f82b7c29ac2cdb815192501418917ee3a57f08dbd37e161e4e51b88","family_id":"qf-congruence-first-mismatch","seed":202610075054,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"16\",\"26\",\"34\"],[\"16\",\"26\",\"50\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(4, 0), A3=(1, 5) and B1=(0, 0), B2=(4, 0), B3=(-1, 5), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"23","explanation":"The ordered squared sides are A=[16, 26, 34] and B=[16, 26, 50]. The first mismatch is 23; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0055","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d4d250c00a60f9fc2cacb7d1b3dbe005ad8bb412db294b5dbe31ee53e42a61f2","family_id":"qf-congruence-first-mismatch","seed":202610075055,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"25\",\"37\",\"52\"],[\"25\",\"37\",\"52\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(5, 0), A3=(1, 6) and B1=(3, 5), B2=(8, 5), B3=(4, -1), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"none","explanation":"The ordered squared sides are A=[25, 37, 52] and B=[25, 37, 52]. The first mismatch is none; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0056","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ecfe7fa76b6f94985698d935308a7db657c06a559b2a749a9a3cc001c156d313","family_id":"qf-congruence-first-mismatch","seed":202610075056,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"36\",\"50\",\"74\"],[\"49\",\"50\",\"85\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(6, 0), A3=(1, 7) and B1=(0, 0), B2=(7, 0), B3=(1, 7), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"12","explanation":"The ordered squared sides are A=[36, 50, 74] and B=[49, 50, 85]. The first mismatch is 12; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0057","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fb8ec3d686f714ee181d827f1ebb28ddbf385723dc23f773ac07dd3f5fddc6d5","family_id":"qf-congruence-first-mismatch","seed":202610075057,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"49\",\"65\",\"100\"],[\"49\",\"82\",\"117\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(7, 0), A3=(1, 8) and B1=(0, 0), B2=(7, 0), B3=(1, 9), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"13","explanation":"The ordered squared sides are A=[49, 65, 100] and B=[49, 82, 117]. The first mismatch is 13; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0058","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"948d800162ccea6055cf0ba8daa7879fa880d70eeecb03fb7c2d4a21d3470383","family_id":"qf-congruence-first-mismatch","seed":202610075058,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"64\",\"82\",\"130\"],[\"64\",\"82\",\"162\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(8, 0), A3=(1, 9) and B1=(0, 0), B2=(8, 0), B3=(-1, 9), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"23","explanation":"The ordered squared sides are A=[64, 82, 130] and B=[64, 82, 162]. The first mismatch is 23; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0059","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"30580a08268daabad78f5149e806b25cd6fff24e7299fa196fadd54811a9515f","family_id":"qf-congruence-first-mismatch","seed":202610075059,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"81\",\"101\",\"164\"],[\"81\",\"101\",\"164\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(9, 0), A3=(1, 10) and B1=(3, 5), B2=(12, 5), B3=(4, -5), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"none","explanation":"The ordered squared sides are A=[81, 101, 164] and B=[81, 101, 164]. The first mismatch is none; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0060","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e0d9ebcba15cc2c5837526b24c59b35f976814a58129d24eb5c3373ee74aa79f","family_id":"qf-congruence-first-mismatch","seed":202610075060,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"100\",\"122\",\"202\"],[\"121\",\"122\",\"221\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(10, 0), A3=(1, 11) and B1=(0, 0), B2=(11, 0), B3=(1, 11), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"12","explanation":"The ordered squared sides are A=[100, 122, 202] and B=[121, 122, 221]. The first mismatch is 12; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0061","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2a29c72128314e523047acb6af276892a3ebf902ca8478ada286fff3b5b10371","family_id":"qf-congruence-first-mismatch","seed":202610075061,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"121\",\"145\",\"244\"],[\"121\",\"170\",\"269\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(11, 0), A3=(1, 12) and B1=(0, 0), B2=(11, 0), B3=(1, 13), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"13","explanation":"The ordered squared sides are A=[121, 145, 244] and B=[121, 170, 269]. The first mismatch is 13; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0062","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d1d9d1162ccf914ea06ddbd68cc6e263a5016f20e03111f49034bce9cd6ec241","family_id":"qf-congruence-first-mismatch","seed":202610075062,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"144\",\"170\",\"290\"],[\"144\",\"170\",\"338\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(12, 0), A3=(1, 13) and B1=(0, 0), B2=(12, 0), B3=(-1, 13), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"23","explanation":"The ordered squared sides are A=[144, 170, 290] and B=[144, 170, 338]. The first mismatch is 23; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0063","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bb7346032c3585a50ecd8f257183109a847e93e1fd07e9321258da33fcc9d5eb","family_id":"qf-congruence-first-mismatch","seed":202610075063,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"169\",\"197\",\"340\"],[\"169\",\"197\",\"340\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(13, 0), A3=(1, 14) and B1=(3, 5), B2=(16, 5), B3=(4, -9), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"none","explanation":"The ordered squared sides are A=[169, 197, 340] and B=[169, 197, 340]. The first mismatch is none; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0064","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b25ac24932ec70d8652e62b598314f603e93921383fdaf09bec5bd814d0d1ebb","family_id":"qf-congruence-first-mismatch","seed":202610075064,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"196\",\"226\",\"394\"],[\"225\",\"226\",\"421\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(14, 0), A3=(1, 15) and B1=(0, 0), B2=(15, 0), B3=(1, 15), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"12","explanation":"The ordered squared sides are A=[196, 226, 394] and B=[225, 226, 421]. The first mismatch is 12; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0065","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8b2b7b24963005ccd4952e0ee0f296cdf1c749c81ea5364912269be1e50c5f13","family_id":"qf-congruence-first-mismatch","seed":202610075065,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"225\",\"257\",\"452\"],[\"225\",\"290\",\"485\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(15, 0), A3=(1, 16) and B1=(0, 0), B2=(15, 0), B3=(1, 17), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"13","explanation":"The ordered squared sides are A=[225, 257, 452] and B=[225, 290, 485]. The first mismatch is 13; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0066","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"49d5e478b17c30adf25fa678061956ad9161eb40175c0cf526fac288d8c6c5ed","family_id":"qf-congruence-first-mismatch","seed":202610075066,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"256\",\"290\",\"514\"],[\"256\",\"290\",\"578\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(16, 0), A3=(1, 17) and B1=(0, 0), B2=(16, 0), B3=(-1, 17), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"23","explanation":"The ordered squared sides are A=[256, 290, 514] and B=[256, 290, 578]. The first mismatch is 23; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0067","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7db1f4024f348699480606c1677315d6f6d0fd7ebbcba4d6aad45c41a72ebd83","family_id":"qf-congruence-first-mismatch","seed":202610075067,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"289\",\"325\",\"580\"],[\"289\",\"325\",\"580\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(17, 0), A3=(1, 18) and B1=(3, 5), B2=(20, 5), B3=(4, -13), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"none","explanation":"The ordered squared sides are A=[289, 325, 580] and B=[289, 325, 580]. The first mismatch is none; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0068","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"98740b81c81275469a6d53424200222fb813493adb5703927f070d32940542d9","family_id":"qf-congruence-first-mismatch","seed":202610075068,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"324\",\"362\",\"650\"],[\"361\",\"362\",\"685\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(18, 0), A3=(1, 19) and B1=(0, 0), B2=(19, 0), B3=(1, 19), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"12","explanation":"The ordered squared sides are A=[324, 362, 650] and B=[361, 362, 685]. The first mismatch is 12; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0069","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5aaeb31b4c53c2fb8efc497b6697cd0e879256808662ca1fba521afb757cfae0","family_id":"qf-congruence-first-mismatch","seed":202610075069,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"361\",\"401\",\"724\"],[\"361\",\"442\",\"765\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(19, 0), A3=(1, 20) and B1=(0, 0), B2=(19, 0), B3=(1, 21), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"13","explanation":"The ordered squared sides are A=[361, 401, 724] and B=[361, 442, 765]. The first mismatch is 13; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0070","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"22763872951fe848e41d1c8b0baa207a2e7236f92cd751017912e566b0fa3ed8","family_id":"qf-congruence-first-mismatch","seed":202610075070,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"400\",\"442\",\"802\"],[\"400\",\"442\",\"882\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(20, 0), A3=(1, 21) and B1=(0, 0), B2=(20, 0), B3=(-1, 21), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"23","explanation":"The ordered squared sides are A=[400, 442, 802] and B=[400, 442, 882]. The first mismatch is 23; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0071","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"918c0d8b4cad675d4a5430175064c0c17714f477c0b7e6a2051a92fd80f10023","family_id":"qf-congruence-first-mismatch","seed":202610075071,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"441\",\"485\",\"884\"],[\"441\",\"485\",\"884\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(21, 0), A3=(1, 22) and B1=(3, 5), B2=(24, 5), B3=(4, -17), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"none","explanation":"The ordered squared sides are A=[441, 485, 884] and B=[441, 485, 884]. The first mismatch is none; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0072","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"196f0a95e444e0a569876dd49864cdb8cdfdad3d2dab7bba056010c465a4fcbd","family_id":"qf-congruence-first-mismatch","seed":202610075072,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"484\",\"530\",\"970\"],[\"529\",\"530\",\"1013\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(22, 0), A3=(1, 23) and B1=(0, 0), B2=(23, 0), B3=(1, 23), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"12","explanation":"The ordered squared sides are A=[484, 530, 970] and B=[529, 530, 1013]. The first mismatch is 12; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0073","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"509509d901d20f55406487c814bdd6e1a89f7f9f75cffc43fd71f3d3b9d9550c","family_id":"qf-congruence-first-mismatch","seed":202610075073,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"529\",\"577\",\"1060\"],[\"529\",\"626\",\"1109\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(23, 0), A3=(1, 24) and B1=(0, 0), B2=(23, 0), B3=(1, 25), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"13","explanation":"The ordered squared sides are A=[529, 577, 1060] and B=[529, 626, 1109]. The first mismatch is 13; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0074","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"05769c9f41b5f7eb3d122c620f35ac1c5c976a17be563d33f7491789978b2351","family_id":"qf-congruence-first-mismatch","seed":202610075074,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"576\",\"626\",\"1154\"],[\"576\",\"626\",\"1250\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(24, 0), A3=(1, 25) and B1=(0, 0), B2=(24, 0), B3=(-1, 25), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"23","explanation":"The ordered squared sides are A=[576, 626, 1154] and B=[576, 626, 1250]. The first mismatch is 23; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0075","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"717b9e9b072a93ead71f99e6b32e9c958b147cd26594d357649e44af4fe70536","family_id":"qf-congruence-first-mismatch","seed":202610075075,"semantic_template":"qf-congruence-first-mismatch/{\"inputs\":[[\"625\",\"677\",\"1252\"],[\"625\",\"677\",\"1252\"]],\"operation\":\"first_mismatch\"}"},"fields":{"title":"First Mismatch in Fixed Corresponding Sides","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(25, 0), A3=(1, 26) and B1=(3, 5), B2=(28, 5), B3=(4, -21), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. In order 12,13,23, give the first label whose corresponding squared side lengths differ. Answer none if all three agree.","answer":{"kind":"short_text","value":"none","explanation":"The ordered squared sides are A=[625, 677, 1252] and B=[625, 677, 1252]. The first mismatch is none; none means agreement in this exact correspondence, without reordering vertices to remove a mismatch."},"skills":["First Mismatch in Fixed Corresponding Sides"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0076","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"81768b37a5045e99d55ae46cc3b89b788a2a8af0e3117a6b28d332be4ad263d0","family_id":"qf-congruence-triangle-validity","seed":202610075076,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"0\",\"0\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(0, 0), A3=(0, 0). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"No","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving No. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0077","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1c21a5a337502230f135be6564f4b27729c34e236e514e8c4fa56ea224610862","family_id":"qf-congruence-triangle-validity","seed":202610075077,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"1\",\"1\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(0, 0), A3=(1, 0). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"No","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving No. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0078","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b9045e7e015f0c2966a5ccb55aa41386436de878e34fb1ee76836095cb8ada29","family_id":"qf-congruence-triangle-validity","seed":202610075078,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"1\",\"1\",\"4\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(1, 0), A3=(2, 0). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"No","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving No. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0079","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"59d3aea58905854a78a09182ce346a50bada33cddfd51b1b0d77a36f9965f246","family_id":"qf-congruence-triangle-validity","seed":202610075079,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"9\",\"17\",\"20\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(3, 0), A3=(1, 4). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"Yes","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving Yes. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0080","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"485bf1c102d8d7ce295b022c65af27291952582bb8f8da8bd48f656d5690ad6f","family_id":"qf-congruence-triangle-validity","seed":202610075080,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"1\",\"16\",\"25\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(4, 0), A3=(5, 0). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"No","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving No. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0081","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4a75072d89c7b4e13835ba1e169b7b959fbe21fcf75642a75c21efc40481aaa3","family_id":"qf-congruence-triangle-validity","seed":202610075081,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"25\",\"25\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(5, 0), A3=(5, 0). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"No","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving No. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0082","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"589f72655367862ccff824a2c315eb02a019ac5b61031e2efadd6a2f449e0298","family_id":"qf-congruence-triangle-validity","seed":202610075082,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"36\",\"50\",\"74\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(6, 0), A3=(1, 7). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"Yes","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving Yes. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0083","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3d848fee68f48652bec26814f5cc792a4f34d4872bc058b84652db24e187fb90","family_id":"qf-congruence-triangle-validity","seed":202610075083,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"1\",\"49\",\"64\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(7, 0), A3=(8, 0). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"No","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving No. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0084","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"93b7488e23b2a940fbb7b4e6a33a5f74cdc4a32b0df5bad72fb484074fedce82","family_id":"qf-congruence-triangle-validity","seed":202610075084,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"64\",\"64\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(8, 0), A3=(8, 0). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"No","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving No. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0085","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"55a41905c2fc6c16d170396744c2d948b26dd50797c5d4ed9d297ef69a082399","family_id":"qf-congruence-triangle-validity","seed":202610075085,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"81\",\"101\",\"164\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(9, 0), A3=(1, 10). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"Yes","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving Yes. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0086","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"92011f90ec2a6d1d9b38f406ed67a64566db8d8a73987f35b3092da6ad10ed9d","family_id":"qf-congruence-triangle-validity","seed":202610075086,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"1\",\"100\",\"121\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(10, 0), A3=(11, 0). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"No","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving No. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0087","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3c45c19a9598ca3e69d549e05bde06c1cc561834732fa44bb1b3d474ba0fb747","family_id":"qf-congruence-triangle-validity","seed":202610075087,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"121\",\"121\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(11, 0), A3=(11, 0). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"No","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving No. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0088","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7283b4e04fc07e23c36b8684a6d428912c1b1be26a14017272243499c57c40f1","family_id":"qf-congruence-triangle-validity","seed":202610075088,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"144\",\"170\",\"290\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(12, 0), A3=(1, 13). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"Yes","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving Yes. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0089","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"96cc19c9dc7daedfa54366fcb3286a448df6cd4d268de6bb42344aa0ad5a05b0","family_id":"qf-congruence-triangle-validity","seed":202610075089,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"1\",\"169\",\"196\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(13, 0), A3=(14, 0). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"No","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving No. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0090","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"54a824b316cd2c261d20a7aa2ae1b8d8ec3a378e12c6d12914498ad18dc9c158","family_id":"qf-congruence-triangle-validity","seed":202610075090,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"196\",\"196\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(14, 0), A3=(14, 0). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"No","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving No. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0091","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b9dd07b1bb1de87e3d3b419992b09906c44d1b0fb14116d58f6195d3a7c05bed","family_id":"qf-congruence-triangle-validity","seed":202610075091,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"225\",\"257\",\"452\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(15, 0), A3=(1, 16). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"Yes","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving Yes. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0092","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"82911c8cc9f90522a00d13c2a160a791f78c230194c63de91f55e692b0a8cbcd","family_id":"qf-congruence-triangle-validity","seed":202610075092,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"1\",\"256\",\"289\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(16, 0), A3=(17, 0). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"No","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving No. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0093","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"82835b1237e5d2a2f90627602768ce26ba643cb58d636d6c046395012e5814c6","family_id":"qf-congruence-triangle-validity","seed":202610075093,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"289\",\"289\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(17, 0), A3=(17, 0). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"No","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving No. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0094","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"87a15126bf46876ba82dbd86df1b0ec7c2f2bc0c8bf7253d7bf9e3d8d64a9665","family_id":"qf-congruence-triangle-validity","seed":202610075094,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"324\",\"362\",\"650\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(18, 0), A3=(1, 19). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"Yes","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving Yes. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0095","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"60ba641c86afe4d437e6ef8a5a994d21e19ccc0825d791291c850e5702bad496","family_id":"qf-congruence-triangle-validity","seed":202610075095,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"1\",\"361\",\"400\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(19, 0), A3=(20, 0). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"No","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving No. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0096","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8683e152cbe3f989b30dd0cf8ee4259c693d0a41dee6995cb0bdf5bb749b437d","family_id":"qf-congruence-triangle-validity","seed":202610075096,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"400\",\"400\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(20, 0), A3=(20, 0). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"No","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving No. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0097","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"53ce21419c885e8cec1467d32b45c655355e047c519926c5584243cf1b9ecfab","family_id":"qf-congruence-triangle-validity","seed":202610075097,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"441\",\"485\",\"884\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(21, 0), A3=(1, 22). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"Yes","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving Yes. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0098","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"789c6759902a0ee101dd085a6ea7e9214be9cd8d9a518dfe7d89079434965c8d","family_id":"qf-congruence-triangle-validity","seed":202610075098,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"1\",\"484\",\"529\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(22, 0), A3=(23, 0). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"No","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving No. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0099","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"036f4b56f7ca8af38782c38fcafc0c768731f890945f4c6a5e3894cbf10a0507","family_id":"qf-congruence-triangle-validity","seed":202610075099,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"0\",\"529\",\"529\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(23, 0), A3=(23, 0). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"No","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving No. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261006-advance-20261007-r05-congruence-0100","batch_id":"batch-20261006-advance-20261007-r05-congruence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e687ef1aafe633d052e62a9184e7e89901f9590f93c86fe992972e879a3d1bc3","family_id":"qf-congruence-triangle-validity","seed":202610075100,"semantic_template":"qf-congruence-triangle-validity/{\"inputs\":[\"576\",\"626\",\"1154\"],\"operation\":\"triangle_validity\"}"},"fields":{"title":"Triangle Eligibility of an Ordered Point Triple","stem":"Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered points are A1=(0, 0), A2=(24, 0), A3=(1, 25). Do they form a nondegenerate triangle of distinct noncollinear points? Reject repeated or collinear data.","answer":{"kind":"short_text","value":"Yes","explanation":"Test whether the determinant of the two differences A2−A1 and A3−A1 is nonzero, giving Yes. Keep this exact coordinate test separate from a visual guess, and do not apply SSS to a degenerate triple."},"skills":["Triangle Eligibility of an Ordered Point Triple"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}