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Question 6
In the below figure, if $Δ A B E ≅ Δ A C D$ , show that $Δ A D E \sim Δ A B C$ .

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Solution

$G i v e n, Δ A B E ≅ Δ A C D$

$∴ A B = A C [B y C P C T] . . . (i)$
$A n d, A D = A E [B y C P C T] . . . (i i)$

In $Δ A D E$ and $Δ A B C$ ,
$\frac{A D}{A B} = \frac{A E}{A C} [D i v i d i n g e q u a t i o n (i i) b y (i)]$
$∠ A = ∠ A [C o m m o n a n g l e]$

$∴ Δ A D E \sim Δ A B C [B y S A S s i m i l a r i t y c r i t e r i o n]$

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