In the given figure $A D$ is the bisector of $∠ A$ and $A B = A C .$ Then $△ A C D$ and $△ A D B$ are congruent by which criterion?

$A S A$

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None of these

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$S S S$

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$S A S$

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Solution

The correct option is D
$S A S$

In $△ A B C$

$A B$ = $A C$ [Given] (equal sides )

$∠ B A D = ∠ C A D$ [because AD is the bisector of angle A] (equal angles)

$A D$ is the common side (equal sides )

Thus, $Δ A B D ≅ Δ A C D$ (SAS Congruency)

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