Question

question 13 (multiple choice worth 1 points) (02.06r mc) if quadrilateral pqrs is a rectangle, then which of the following is true? (overline{ps}congoverline{qr}) (angle psqcongangle qsr) (overline{sr}congoverline{rq}) (overline{ps}congoverline{pr})

Explanation:

Step1: Recall rectangle properties

In a rectangle, opposite sides are congruent.

Step2: Analyze each option

• Option 1: $\overline{PS}$ and $\overline{QR}$ are opposite sides of rectangle $PQRS$. By the property of a rectangle, opposite - sides are congruent. So $\overline{PS}\cong\overline{QR}$.
• Option 2: $\angle PSQ$ and $\angle QSR$ are not necessarily congruent. Diagonals of a rectangle bisect each other but do not necessarily bisect the angles of the rectangle.
• Option 3: $\overline{SR}$ and $\overline{RQ}$ are adjacent sides of the rectangle. Adjacent sides of a rectangle are not congruent (except in the case of a square, but we are not given that it is a square).
• Option 4: $\overline{PS}$ is a side and $\overline{PR}$ is a diagonal. A side and a diagonal of a rectangle are not congruent.

Answer:

$\overline{PS}\cong\overline{QR}$