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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
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Solution
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.
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