Question

consider quadrilateral wxyz. based on the information given, is the quadrilateral a parallelogram? explain. the figure is a parallelogram because there are two pairs of congruent sides. the figure is a parallelogram because a diagonal is bisected. the figure is not necessarily a parallelogram because the diagonals are not congruent. the figure is not necessarily a parallelogram because only one diagonal is bisected and only one pair of sides is congruent.

Explanation:

Step1: Recall parallelogram properties

A parallelogram has two - pairs of parallel sides, two - pairs of congruent sides, and diagonals that bisect each other.

Step2: Analyze given information

The figure shows one diagonal bisected and one pair of congruent sides. But for a quadrilateral to be a parallelogram, we need both diagonals bisected or two - pairs of congruent sides (among other properties). One diagonal bisected and one pair of congruent sides are not sufficient conditions.

Answer:

The figure is not necessarily a parallelogram because only one diagonal is bisected and only one pair of sides is congruent.