Question

In the below figure, if $\Delta ABE\cong \Delta ACD$, show that $\Delta ADE\sim \Delta ABC$.

Answer 1

$Given,\Delta ABE\cong \Delta ACD$

$\therefore AB=AC\left[ByCPCT\right]...\left(i\right)$
$And,AD=AE\left[ByCPCT\right]...\left(ii\right)$

In $\Delta ADE$ and $\Delta ABC$,
$\frac{AD}{AB}=\frac{AE}{AC}\left[Dividingequation\right(ii\left)by\right(i\left)\right]$
$\angle A=\angle A\left[Commonangle\right]$

$\therefore \Delta ADE\sim \Delta ABC\left[BySASsimilaritycriterion\right]$