Question

In the adjoining figure, show that $ABCD$ is a parallelogram.

Answer 1

REF.IMAGE

From the figure

$\Delta ABD$ and $\Delta BCD$ is clear that

$AB=CD-5cm$ (given)

$AB=AB$ (common side)

and

$\angle ABD=\angle CDB$(alternate angle)

so, $ABC\cong BCD$ (SAS fule)

So, $AD=BC\left(CPCT\right)$

Hence $AB=CD$

$AD=BC$

Opposite sides are equal and parallel.

So it is a parallelogram.