Question

In the given figure, $△ABC$ is an isosceles triangle in which $AB=AC$. If $AB$ and $AC$ are produced to $D$ and $E$ respectively such that $BD=CE$.
Prove that $BE=CD.$

Answer 1

Given: $ABC$ is an isosceles triangle.

$AB=AC$ and $BD=BE$

To prove: $BE=CD$

Proof: As, $AB=AC,BD=CE$

$AB+BD=AC+CE$ [Adding the above two equations]

$\Rightarrow AD=AE$

Consider $△ACD$ and $△ABE$, we have

$AC=AB$ (given)

$\angle CAD=\angle BAE$ (common)

$AD=AE$ (proved above)

$△ACD\cong △ABE$ [By SAS congruence property]

$CD=BE$ (corresponding parts of the congruent triangles)