Question

In triangle ABC, AB = AC; BE $\perp$ AC and CF $\perp$ AB. Prove that :

(i) BE =CF

(ii) AF = AE

Answer 1

(i)

$\angle A$=$\angle$A
$\angle$AEB=$\angle$AFC=90 Degree
AB=AC
from AAS
Triangle AEB congruent Triangle AFC
BE=CF
(ii)Since

Triangle AEB congruent Triangle AFC

$\angle$ABE=$\angle$ACF
So
AF=AE