Question

In the given figure, $△ABC$ is an isosceles with AB = AC, D and E are points on BC such that BE = CD. show that AD=AE.

Answer 1

Given an isosceles triangle $△ABC$,

$\therefore AB=AC$

Also, $BE=CD$

We have to prove that $AD=AE$

Since, $AB=AC$

$\therefore \angle C=\angle B$ [Angles opposite to equal sides are equal] .... (1)

In $△ACD$ and $△ABE$,

$AC=AB$ (Given)

$\angle C=\angle B$ (From (1))

$CD=BE$ (Given)

So, $△ACD\cong △ABE${ SAS congruence rule}

$\therefore AD=AE${ By CPCT}

Hence proved.