# BD and CE are bisectors of ∠B and ∠C of an isosceles Δ ABC with AB = BC. Prove that BD = CE.

Given,

In isosceles Δ ABC,

BD and CE are bisectors of B and C

And,

AB = AC

To prove: BD = CE

Proof: In Δ BEC and Δ CDB, we have

B =C (Angles opposite to equal sides)

BC = BC (Common)

BCE = CBD (Since, C = B C = B BCE = CBD)

By ASA theorem, we have

Δ BEC Δ CDB

EC = BD (By c.p.c.t)

Hence, proved

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