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SAS Criteria for Congruency

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

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Solution

(i) In $Δ A B D$ and $Δ B A C$ ,
$A D = B C$ (Given)
$∠ D A B = ∠ C B A$ (Given)
$A B = B A$ (Common)
$∴ Δ A B D ≅ Δ B A C$ (By SAS congruence rule)
(ii) $∴ B D = A C$ (By CPCT)
(iii) And, $∠ A B D = ∠ B A C$ (By CPCT)

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ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (See the given figure). Prove that

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(ii) BD = AC

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$∠ A B D = ∠ B A C$

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