Question

In the given figure, ABCD is a quadrilateral such that $AB||CD$ and $BC||AD.$


Gaurav says that AB = CD and Jatin says that AD = BC. Who is correct?

• A. Only Gaurav
• B. Only Jatin
• C. Both Gaurav and Jatin
• D. Neither Gaurav nor Jatin

Answer 1

The correct option is C Both Gaurav and Jatin

Given: In quadrilateral $ABCD,AB||CD$ and $BC||AD$.



Here $BD$ is a transversal. So, we get,



In $\Delta ABD$ and $\Delta CDB$,
$AB||CD$
$\Rightarrow \angle 1=\angle 2$ (alternate interior angles)
$AD||BC$
$\Rightarrow \angle 3=\angle 4$(alternate interior angles)
$BD=BD$ (common)
$\therefore \Delta ABD\cong \Delta CDB$ (by ASA congruence criterion)
So, we have $AB=CD$ and $AD=BC$ by CPCT.
Thus, both Gaurav and Jatin are correct.
Therefore, the correct answer is (c).