Question

quadrilateral rstu has one pair of opposite parallel sides and one pair of opposite congruent sides as shown. based on the given information, which statement best explains whether the quadrilateral is a parallelogram? it cannot be determined from the information given. it is not a parallelogram because the congruent sides cannot be parallel. it is not a parallelogram because the parallel sides cannot be congruent. it is a parallelogram based on the single opposite side pair theorem.

Explanation:

A parallelogram requires both pairs of opposite sides to be parallel. Here, only one pair of opposite sides is parallel. Just having one pair of parallel and one pair of congruent sides is not sufficient to confirm it as a parallelogram. Also, there's no rule that congruent sides can't be parallel (in a parallelogram, congruent sides are parallel) or that parallel sides can't be congruent (again, in a parallelogram they are). Since the key property (two - pairs of parallel sides) is not met and we can't be sure from the given info (one - pair parallel and one - pair congruent) if it's a parallelogram.

Answer:

It cannot be determined from the information given.