Question

Your friend​ says, "If a quadrilateral has a pair of opposite sides that are congruent and a pair of opposite sides that are​ parallel, then it is a​ parallelogram." What is your​ friend's error? Explain.

Choose the correct answer below.

A quadrilateral is a parallelogram if the pair of longer sides congruent and the pair of shorter sides parallel.

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

A quadrilateral is a parallelogram if one pair of opposite sides is parallel.

Answer 1

The correct answer is: "A quadrilateral is a parallelogram if one pair of opposite sides are congruent and parallel."

This is because the statement made by the friend is incorrect as it is not necessary for both pairs of opposite sides to be congruent for a quadrilateral to be a parallelogram. All that is required is for one pair of opposite sides to be both congruent and parallel.