Question

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

Answer 1

Step-by-step explanation:

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Answer 2

Given: BD and CE are bisectors of ∠B and ∠C of an isosceles Δ ABC with AB = AC.

To prove :  BD = CE

Proof:

In Δ BEC and Δ CDB, we have

∠B =∠C  

[Angles opposite to equal sides are equal]

BC = BC (Common)

∠BCE = ∠CBD  

[Since, ∠C = ∠B,  1/2∠C = 1/2∠B , ∠BCE = ∠CBD]

Therefore, Δ BEC  ≅  Δ CDB (by ASA congruence rule)

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

Hence, proved

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