Question

In ∆ABC, AB = AC.
BE & CF are altitudes.
Prove that BE = CF.

Answer 1

In ∆ABE &∆ ACF,                                         AB=AC. (Given)                                                                Angle BAE= Angle CAF (common).                   Angle AEB=Angle AFC =90°.                     ∆ABE~∆ACF (AAS)                                   BE=CF (CPCT)                                           Hence proved.

Answer 2

In triangle ABE and triangle ACF,

AB = AC (given)

angle AEB = angle AFC (altitudes)

angle A = angle A (common)

Therefore triangle ABE ≅ triangle ACF (AAS rule)

From this,

BE = CF (CPCT)