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SAS Similarity

ABCD is quadr...

Question

$A B C D$ is 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

In triangles $A B D$ and $A B C$

$A D = B C$ (given )

$∠ B A D = ∠ A B C$ ( given )

$A B = A B$ ( common )

By SAS criterion of congruency $△ A B D$ is congruent to $△ A B C$

$B D = A C$ (by CPCT )

$∠ A B D = ∠ B A C$ ( 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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$A B C D$ is a quadrilateral in which $A D = B C$ and $∠ D A B = ∠ C B A$ prove that
$∠ A B D = ∠ B A C$

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