Q. 184.0( 2 Votes )

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Answer :

Given: AB=AC and BD and AB are angle bisectors of ∠B and ∠C

To prove: BD = CE

Proof:

In ∆ABD and ∆ACE,

∠ABD = ∠B

And ∠ACE = ∠C

But ∠B = ∠C as AB = AC … As in isosceles triangle, base angles are equal

∠ABD = ∠ACE

AB = AC

∠A = ∠A

Thus by ASA property of congruence,

∆ABD ≅ ∆ACE

Hence, we know that, corresponding parts of the congruent triangles are equal

∴ BD = CE

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