In the below quadrilateral ABCD, if AD = BC and ∠DAB = ∠CBA, then what is t

Question

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

Options:

A . ∠ABD = ∠BAC

B . ∠ABD

C . ∠ABD > ∠BAC

D . ∠DAB = ∠BAC

Answer: Option A
:
A
In

Δ A B D and 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).
Thus,

∠ A B D

∠ B A C

(congruent parts of congruent triangles).

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