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Opposite Sides of a Parallelogram Are Equal

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 $B D = A C .$

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Solution

In $△ A B D$ and $△ B A C,$
$A D = B C$ [ Given ]
$∠ D A B = ∠ C B A$ [ Given ]
$A B = B A$ [ Common side ]

So, by the Side-Angle-Side criterion of congruence,
$△ A B D ≅ △ B A C$

$∴$ $B D = A C$ [CPCT]

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