Question

Use the definition of a parallelogram to complete the biconditional statement.

A parallelogram is a quadrilateral with two pairs of parallel sides.

A quadrilateral is a parallelogram _[blank]_.

Which answer correctly fills in the blank in the previous sentence?


if it has two pairs of parallel sides and is a polygon


if and only if it has two pairs of parallel sides


because it has only four sides and two of them are parallel


if it has only two pairs of parallel sides

Answer 1

if and only if it has two pairs of parallel sides

Explanation:

The definition says that a paralellogram is a quadrilateral with two pairs of parallel sides. That means that the only way to have a paralellogram is to have a quadrilateral with two pairs of parallel sides. If we have a quadrilateral with only one pair of parallel sides, then it is not a parallelogram.

This translates to the following statement "a quadrilateral is a parallelogram if and only if it has two pairs of parallel sides". Meaning that if we have a parallelogram we know we have a quadrilateral with two pairs of parallel sides and if we have a quadrilateral with two pairs of parallel sides we have a parallelogram.