Question

In the following figure, if ΔABE≅ΔACD, show that ΔADE ~ ΔABC.

Answer 1

It is given that ∆ABE ≅ ∆ACD.
∴ AB = AC [By CPCT]…(1)
And, AD = AE [By CPCT].... (2)
In ∆ADE and ∆ABC,
$\frac{AD}{AB}=\frac{AE}{AC}$ [Dividing equation (2) by (1)]
$\angle$A = $\angle$A [Common angle]
∴ ∆ADE ∼ ∆ABC [By SAS similarity criterion]