Q. 184.0( 2 Votes )

# ABC is a triangle in which AB=AC. If the bisectors of ∠B and ∠C meet AC and AB in D and E respectively, prove that BD=CE.

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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