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ABCD is a qua...

Question

$A B C D$ is a quadrilateral in which $A D = B C$ and $∠ D A B = ∠ C B A$ . Prove that
$(i) △ A B D ≅ △ B A C$
$(i i) B D = A C$
$(i i i) ∠ A B D = ∠ B A C .$

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Solution

In $△ A B D, △ B A C$
$A D = B C$
$∠ D A B = ∠ C B A$
$A B = B A$
By $S . A . S$ criteria of congruency
$△ A B D ≅ △ B A C$
$⟹ B D = A C$ ...CPCT
$⟹ ∠ A B D = ∠ B A C$ ...CPCT

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