Question

BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.

Answer 1

It is given that

Is bisector of and is bisector of.

And is isosceles with

We have to prove that

If will be sufficient to prove to show that

Now in these two triangles

Since, so

Now as BD and CE are bisector of the respectively, so

, and

BC=BC

So by congruence criterion we have

Hence Proved.