prove-geometric-theorem

Prove geometric theorems using Euclidean axiomatic methods, coordinate geometry, or vector methods with rigorous step-by-step logical structure. Covers direct proof, proof by contradiction, coordinate proofs, vector proofs, and handling of special cases and degenerate configurations. Use when given a geometric statement to prove, verifying a conjecture, establishing a lemma, converting geometric intuition into a rigorous proof, or comparing the effectiveness of different proof methods.