Question

In fig, If $\Delta ABE\cong \Delta ACD$, show that $\Delta ADE$ is similar to $\Delta ABC$

Answer 1

REF.Image

Given

$\Delta ABE\cong \Delta ACD$

Hence, $AB=AC$ -------- (1)

and $AE=AD$

i.e, $AD=AE$ ---------- (2)

Now Divide (2) by (1)

$\frac{AD}{AB}=\frac{AE}{AC}------\left(3\right)$

In $\Delta ADE$ and $\Delta ABC$

$\angle A=\angle A$ (common angle)

$\frac{AD}{AB}=\frac{AE}{AC}$ (from 3)

$\therefore \Delta ADE\sim \Delta ABC$ (SAS similarity criterion)

Hence Proved.