AD and BE are respectively altitudes of a triangle ABC such that AE=BD. Prove that AD=BE.

Given: AE = BD; AD and BE are altitudes of ΔABC.

To Prove: AD = BE

Proof: 

In ΔABD and ΔABE,

AB = AB  (Common Hypotenuse)

BD = AE  (Given)

∠ADB = ∠AEB  (Right-angle)

Thus,  ΔABD is congruent to ΔABE by RHS congruency rule.

Hence, AD = BE  (By CPCT)

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