Question

In triangle ABC, AB is equal to AC ,
BE perpendicular to AC
and CF is perpendicular to AB.
Prove that:
1. BE=CF
2. AF=AE​

Answer 1

1.to prove BE = CF

given : angle 1=angle 2= 90°

angle 3=angle 4 ( base angles)

in triangle BFC & triangle CEB

angle1=2

angle 3=4

BC=BC (common )

by AAS

BE =CF (cpct)

2. to prove AE =AF

AB = AC given

FB = BC (cpct)

AF +FB=AE +BC

FB and BC are cancelled

therefore AF= AE