Question

In the adjoining figure, $D$ and $E$ are points on the side $BC$ of $△ABC$ such that $BD=EC$ and $AD=AE$. Show that $△ABD\cong △ACE$.

Answer 1

$AD=AE\Rightarrow \angle ADE=\angle AED$$\Rightarrow {180}^o-\angle ADE={180}^o-\angle AED$$\Rightarrow \angle ADB=\angle AEC$.$△ABD\cong △ACE$ (SAS).