Question

rectangle pqrs has diagonals $overline{pr}$ and $overline{qs}$. move options into the table to prove that diagonals $overline{pr}$ and $overline{qs}$ are congruent.

statement	reason
	interior angles of rectangles are congruent.
	opposite sides of a rectangle are congruent.
	reflexive property
$overline{pr}congoverline{qs}$	corresponding parts of congruent triangles are congruent

$angle psrcongangle qrs$ $angle psrcongangle rqp$ $overline{pq}congoverline{rs}$ $overline{pr}congoverline{pr}$ $overline{ps}congoverline{qr}$

Explanation:

Step1: Identify angle - congruence

$\angle PSR\cong\angle QRS$ because interior angles of rectangles are congruent.

Step2: Identify side - congruence

$\overline{PQ}\cong\overline{RS}$ since opposite sides of a rectangle are congruent.

Step3: Identify common side

$\overline{SR}\cong\overline{RS}$ by the reflexive property.

Step4: Prove triangle congruence

$\triangle PSR\cong\triangle QRS$ by Side - Angle - Side (SAS) congruence criterion.

Step5: Prove diagonal congruence

Since $\triangle PSR\cong\triangle QRS$, $\overline{PR}\cong\overline{QS}$ (corresponding parts of congruent triangles are congruent).

Answer:

Statement	Reason
$\angle PSR\cong\angle QRS$	Interior angles of rectangles are congruent.
$\overline{PQ}\cong\overline{RS}$	Opposite sides of a rectangle are congruent.
$\overline{SR}\cong\overline{RS}$	Reflexive property
$\triangle PSR\cong\triangle QRS$	SAS congruence criterion (from previous steps)
$\overline{PR}\cong\overline{QS}$	Corresponding parts of congruent triangles are congruent