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]