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SAS Criteria for Congruency

ABCD is a qua...

Question

ABCD 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

Given:
$A D = B C ∠ D A B = ∠ C B A$

(i) $Consider △ A B D and △ B A C A B = A B (Common) ∠ D A B = ∠ C B A (Given) A D = B C (Given) By SAS congruence criteria, △ A B D ≅ △ B A C$

(ii) $B D = A C (By CPCT)$
(iii) $∠ A B D = ∠ B A C (By CPCT)$

Hence Proved.

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