Question

In the following figure, AB = AC and AD is perpendicular to BC. BE bisects angle B and EF is perpendicular to AB.
Prove that :  ED = EF 

Answer 1

In ΔEFB and ΔEDB,
∠EFB = ∠EDB ( both are 90⁰ )
EB = EB ( common side )
∠FBE = ∠DBE ( given )
ΔEFB ≅ ΔEDB  (AAS congruence criterion)
⇒ EF = ED (cpct )
that is , Ed = EF.