Question

choose all answers that describe the quadrilateral pqrs if $overline{pq}paralleloverline{rs}$, $pq = 8$, and $rs = 8$.
answer
attempt 1 out of 2
□ parallelogram
□ rectangle
□ rhombus
□ square
□ trapezoid

Explanation:

Step1: Recall the properties of quadrilaterals

A parallelogram is a quadrilateral with two - pairs of parallel sides. Given that $\overline{PQ}\parallel\overline{RS}$ and $PQ = RS=8$, one pair of opposite sides is parallel and equal. So, it satisfies the condition for a parallelogram.

Step2: Analyze other quadrilaterals

A rectangle is a parallelogram with four right - angles. There is no information about the angles, so we cannot conclude it is a rectangle. A rhombus is a parallelogram with all sides equal. There is no information about the other two sides, so we cannot conclude it is a rhombus. A square is a rectangle and a rhombus, so without information about angles and other side - lengths, we cannot conclude it is a square. A trapezoid is a quadrilateral with exactly one pair of parallel sides. But since we have a parallelogram (a more specific case), it is not a trapezoid (a trapezoid has non - parallel sides in the general sense).

Answer:

A. Parallelogram