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SAS Criteria for Congruency

In the below ...

Question

In the below quadrilateral ABCD, if AD = BC and $∠ D A B$ = $∠ C B A$ , then what is the relation between $∠ A B D$ and $∠ B A C$ ?

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Solution

In $Δ A B D and Δ B A C$ ,
AD = BC (Given)
$∠ B A D$ = $∠ C B A$ (Given)
AB = BA (Side common to both triangles)
Hence $Δ A B D \sim Δ B A C$
(by SAS similarity condition)
Thus, $∠ A B D$ = $∠ B A C$
(Corresponding parts of similar triangles)

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