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geometry proofs

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given ABC is a triangle. Ad is the altitude to BC. Ad biscects angle BAC.

Prove: Ad is the median to BC

  • geometry proofs -

    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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