Posted by SKipper on Tuesday, December 14, 2010 at 12:25am.
given ABC is a triangle. Ad is the altitude to BC. Ad biscects angle BAC.
Prove: Ad is the median to BC

geometry proofs  MathMate, Tuesday, December 14, 2010 at 9:02am
Consider triangles ABd and ACd for congruence:
Ad is altitude, so
∠ABd = ∠ACd = 90°
Ad bisects angle BAC, so
∠CAd = ∠BAd
Ad = Ad (common side)
So triangles ABd and ACd are congruent, ASA (anglesideangle).
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