In the given figure, AD is the bisector of $∠$ A and AB = AC. Prove that $△$ ACD and $△$ ABD are congruent.

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Solution

In $△$ ACD and $△$ ABD

$∠ B A D = ∠ C A D$
[ $∵$ AD is the bisector of $∠ A$ ]
AD = AD [common side]
AB = AC [Given]

$△ A C D ≅ △ A B D$ [SAS congruency]
The triangles are congruent by SAS congruence rule.

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