Question

A quadrilateral is a parallelogram if a pair of its opposite sides are parallel and congruent.

• A. True
• B. False

Answer 1

The correct option is A True

$AC$ is a transversal and also $AB║CD$, therefore

$\angle BAC=\angle DCA$(Alternate angles)

In $\Delta ADC$ and $\Delta CBA$, we have

$AB=CD$(Given)

$\angle BAC=\angle DCA$(Alternate angles)

$AC=CA$(Common)

$\Delta ADC\cong \Delta CBA$ by the SAS rule.

Hence, by CPCT, $DA=BC$ and $DC=AB$

Thus, a pair of opposite side is parallel and congruent in quadrilateral ABCD, therefore ABCD is a parallelogram.

Hence proved.