In the quadrilateral ABCD, if AD = BC and $∠ D A B$ = $∠ C B A$ , then relation between $∠ A B D$ and $∠ B A C$ is

∠ABD = ∠BAC

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∠ABD < ∠BAC

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∠ABD > ∠BAC

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∠DAB =∠BAC

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Solution

The correct option is A
∠ABD = ∠BAC

In $Δ A B D a n d Δ B A C$ ,

AD=BC, (Given)

$∠ B A D$ = $∠ C B A$ , (Given)

AB=BA (Side common to both triangles)

Hence, $Δ A B D ≅ Δ B A C$ (by SAS congruence condition).

$∴$ $∠ A B D$ = $∠ B A C$ (congruent parts of congruent triangles).

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In the below quadrilateral ABCD, if AD = BC and $∠ D A B$ = $∠ C B A$ , then,

In the below quadrilateral ABCD, if AD = BC and $∠ D A B$ = $∠ C B A$ , then what is the relation between $∠ A B D$ and $∠ B A C$ ?

A B C D

A D = B C

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△ A B D ≅ △ B A C

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