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Opposite Sides of a Parallelogram Are Equal

ABCD is a qua...

Question

ABCD is a quadrilateral in which $A D = B C$ and $∠ D A B = ∠ C B A$ . Then:

△ A B C ≅ △ B A D

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B D = A C

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∠ A B D = ∠ B A C

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None of these

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Solution

The correct options are
B $B D = A C$
C $∠ A B D = ∠ B A C$
D $△ A B C ≅ △ B A D$
In $△ A B C$ and $△ B A C$ ,
$A D = B C$ (Given)
$∠ D A B = ∠ C B A$ (Given)

$A B = A B$ (Common side)
$∴$ By SAS congruence rule, $△ A B C ≅ △ B A C$
Also, by CPCT, we have $B D = A C$ and $∠ A B D = ∠ B A C$

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