Posted by SKipper on .
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,
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).