Question

In the below quadrilateral ABCD, if AD = BC and $\angle DAB$ = $\angle CBA$, then,

• A. ∠ABD = ∠BAC
• B. ∠ABD < ∠BAC
• C. ∠ABD > ∠BAC
• D. ∠DAB =∠BAC

Answer 1

The correct option is A

∠ABD = ∠BAC

In $\Delta ABD$ and $\Delta BAC$,
AD=BC, (Given)
$\angle BAD$ = $\angle CBA$, (Given)
AB=BA; (Side common to both triangles)
Hence, $\Delta ABD\cong \Delta BAC$ (by SAS congruence condition).
Thus, $\angle ABD$ = $\angle BAC$ (congruent parts of congruent triangles).