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SSS Rule

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) $△ A B D ≅ △ B A C$
(ii) $B D = A C$
(iii) $∠ A B D = ∠ B A C$

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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)

$∴ △ A B D ≅ △ B A C$ (By SAS congruence rule)

$∴ B D = A C$ (By CPCT)

And, $∠ A B D = ∠ B A C$ (By CPCT)

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