Question

BD and CE are bisectors of $\angle Band\angle C\text{of an isosceles}\Delta ABCwithAB=AC.$ Prove that BD = CE.

Answer 1

Given : In $\Delta ABC,AB=AC$

BD and CE are the bisectors of $\angle Band\angle Crespectively$

To prove : BD = CE

Proof : In $\Delta ABC,AB=AC$

$\therefore \angle B=\angle C$ (Angles opposite to equal sides)

$\therefore \frac{1}{2}\angle B=\frac{1}{2}\angle C$

$\angle DBC=\angle ECB$

Now, in $\Delta DBCand\Delta EBC,$

BC = BC (Common)

$\angle C=\angle B$ (Equal angles)

$\angle DBC=\angle ECB$ (Proved)

$\therefore \Delta DBC\cong EBC$ (ASA axiom)

$\therefore BD=CE$