Explore related knowledge and questions →
← Question derivation index · Original question batch
R0070-35662 · q-20260912-right-triangle-determination-0012
A nondegenerate triangle has interior angles 65°, 80°, 35°. Is it a right triangle?
G001 — A nondegenerate triangle has interior angles 65°, 80°, 35°. Is it a right triangle?Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
source roles = [qf-right-triangle-determination, [angles, mode]]
After
derived = [right, null, null]
Conditions: none
Use THIS bank’s actual fields,operation/domain and types.BASE retains permissible extra metadata.Do not import LDL SAFE/set limits or a different bank’s deduplication rules.
Rule: R70_SOURCE_bank_specific_interface · Uses: G001
Before
Right triangle ORIGINAL three interior angles sum := sum(65, 80, 35)
After
Right triangle ORIGINAL three interior angles sum = 180
Conditions: none
This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation.
Rule: exact_rational_arithmetic · Uses: G001, S001
Before
source roles = [[65, 80, 35], 180]
After
derived = [[No, No, No], No]
Conditions: none
ALL30 actual questions have THREE positive interior angles summing to180,matching the bilingual nondegenerate-triangle premise.A right triangle is defined by ONE angle of90.First qualify the triangle;90 in invalid angle data is not enough.
Rule: Right_triangle_GIVEN_nondegenerate_angle_sum_then_definition · Uses: G001, S002
S003 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.S002 · premise_and_result_audit — Recompute Right triangle ORIGINAL three interior angles sum with exact rational arithmetic, not rounded decimals.S001 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.No
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 0acf0783ca8060c9082f8539a0877cb4c7bcf5c78ec210858a1c1946355b14abcandidate record SHA-256: 6fb7d7b0b9773357de0df0529dcdbc991f7d751677b755ce5b3368f59390367bsemantic review receipt SHA-256: 9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80question-first witness SHA-256: c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dabLean: NOT_RUN · human review: NOT_PERFORMED