Homework Help: geometry proofs

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 (angle-side-angle).

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