{"schema_version":"ocme-site-results-v1","locale":"zh-Hant","page_type":"paths","facts":{"questions":36000,"reviewed":36000,"display_candidates":0,"knowledge":302,"guides":299,"paths":59,"batches":360,"families":1441,"atlas":302,"core":80,"evidence":9,"formal_evidence":5,"formal_subjects":4,"lean_files":6,"lean_toolchain":"leanprover/lean4:v4.30.0","question_state":"candidate","english_state":"ai_candidate","question_Lean":"NOT_RUN","canonical_truth_promotion":false},"filters":{},"path":{"id":"path-geometry-foundations","title":{"zh-Hant":"幾何基礎到畢達哥拉斯定理","en":"Geometry Foundations to the Pythagorean Theorem"},"summary":{"zh-Hant":"由點、線、面的基礎語言，經三角形、角、長度與直角三角形進入畢達哥拉斯定理。","en":"Move from the language of points, lines, and planes through triangles, angles, length, and right triangles to the Pythagorean theorem."},"audience":["general_learner","upper_secondary"],"review":"candidate","nodes":[{"id":"mko-point-line-plane","position":1,"requirement":"required","rationale":{"zh-Hant":"先區分幾何位置、延伸對象與圖示。","en":"First distinguish geometric positions, extended objects, and their diagrams."}},{"id":"mko-triangle","position":2,"requirement":"required","rationale":{"zh-Hant":"由三個相異不共線點建立三角形、頂點與邊。","en":"Build a triangle, its vertices, and its sides from three distinct noncollinear points."}},{"id":"mko-angle","position":2,"requirement":"required","rationale":{"zh-Hant":"建立共同端點兩射線與角量的語言。","en":"Establish the language of two rays with a common endpoint and angle measure."}},{"id":"mko-euclidean-length","position":2,"requirement":"required","rationale":{"zh-Hant":"平行建立邊長與距離的意義。","en":"In parallel, establish the meaning of side length and distance."}},{"id":"mko-right-triangle","position":3,"requirement":"required","rationale":{"zh-Hant":"再以直角與邊確定定理適用的幾何對象。","en":"Use a right angle and sides to identify the geometric object to which the theorem applies."}},{"id":"mko-euclid-pythagorean-theorem","position":4,"requirement":"required","rationale":{"zh-Hant":"最後理解平方關係與證明。","en":"Finally understand the squared relation and its proof boundaries."}}]},"title":"幾何基礎到畢達哥拉斯定理"}