Question

Question 6
In the below figure, if $\Delta ABE\cong \Delta ACD$, show that $\Delta ADE\sim \Delta ABC$.

Answer 1

It is given that $\Delta ABE\cong \Delta ACD$.
$\therefore AB=AC\left[ByCPCT\right]...\left(i\right)$
And, AD = AE [By CPCT] ... (ii)
In $\Delta ADE$ and $\Delta ABC$,
$\frac{AD}{AB}=\frac{AE}{AC}$ [Dividing equation (ii) by (i)]
$\angle A=\angle$ A [Common angle]
$\therefore \Delta ADE\sim \Delta ABC$ [By SAS similarity criterion]