ABCD is a quadrilateral in which AD = BC and $∠ D A B = ∠ C B A$ (See the given figure). Prove that
$∠ A B D = ∠ B A C .$

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Solution

$I n Δ A B D a n d Δ B A C, A D = B C (G i v e n) ∠ D A B = ∠ C B A (G i v e n) A B = B A (C o m m o n) ∴ Δ A B D ≅ Δ B A C (B y S A S c o n g r u e n c e r u l e) ∴ ∠ A B D = ∠ B A C (B y C P C T)$

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∠ D A B = ∠ C B A

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