In the given figure, if AB = DC, $∠ A B D = ∠ C D B$ , which congruence rule would you apply to prove $Δ A B D = Δ C D B$ ?

SAS

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ASA

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RHS

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SSS

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Solution

The correct option is B SAS
In $△ A B D$ and $△ C D B$
$A B = C D$ (given)
$∠ A B D = ∠ C D B$ (given)
$B D = D B$ (common side)
$∴ △ A D B ≅ △ C D B$ by $S A S$ criteria.
So option $A$ is correct.

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