In fig. $Δ A B D ≅ Δ A C D, A B = A C$ .
Name the criteria by which the triangles are congruent.

S S S

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R H S

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S A S

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A S A

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Solution

The correct option is A $S S S$
In $△ A B D$ and $△ A C D$ ,
$A B = A C$ (given)
$B D = C D$ (given)
$A D = A D$ (common side)
Here, the three corresponding sides of the given triangles are equal.
$∴ △ A B D ≅ A C D$ by $S S S$ congruency criteria.

Hence, option $A$ is correct.

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