Question

In the below quadrilateral ABCD, if AD = BC and $\angle DAB$ = $\angle CBA$, then what is the relation between $\angle ABD$ and $\angle BAC$ ?

• A. $\angle ABD$ = $\angle BAC$
• B. $\angle ABD$ < $\angle BAC$
• C. $\angle ABD$ > $\angle BAC$
• D. $\angle DAB$ = $\angle BAC$

Answer 1

The correct option is A

$\angle ABD$ = $\angle BAC$

In $\Delta ABD\text{and}\Delta BAC$,
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, $\angle ABD$ = $\angle BAC$
(corresponding parts of congruent triangles).