In the given figure, $∆ A B C$ is an isosceles triangle such that $A B = A C .$ $A D$ and $A E$ are lines making $∠ 1 = ∠ 2$ Prove that $∆ A B E ≅ ∆ A C D$

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Solution

Step-1: Given Information
$∆ A B C$ is an isosceles triangle such that $A B = A C .$
So, $∠ A C D = ∠ A B E$ (as opposite angles to equal sides of an isosceles triangle are equal)
$∠ 1 = ∠ 2$
Step-2: In $∆ A C D$ and $∆ A B E$
$∠ 1 = ∠ 2$ (given)
$∠ A C D = ∠ A B E$
$A C = A B$ (given)
Hence, $∆ A C D ≅ ∆ A B E$ (by $A A S$ Congruency)

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