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

∠ A B D

∠ B A C

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∠ A B D

∠ B A C

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∠ A B D

∠ B A C

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∠ D A B

∠ B A C

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Solution

The correct option is A $∠ A B D$ = $∠ B A C$
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, $Δ A B D ≅ Δ B A C$
by SAS criterion for congruency of triangles.

Thus, $∠ A B D$ = $∠ B A C$
(congruent parts of congruent triangles).

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