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

| statement | reason |
| --- | --- |
| $pqrs$ is a rectangle. | given |
| | interior angles of rectangles are congruent. |
| | opposite sides of a rectangle are congruent. |
| | reflexive property |
| | |
| $\overline{pr} \cong \overline{qs}$ | corresponding parts of congruent triangles are congruent. |

$\angle psr \cong \angle qrs$ $\angle psr \cong \angle rqp$ $\overline{pq} \cong \overline{rs}$ $\overline{pr} \cong \overline{pr}$ $\overline{ps} \cong \overline{qr}$ $\overline{rs} \cong \overline{sr}$
$\triangle prs \cong \triangle rpq$ $\triangle prs \cong \triangle qsr$
aas congruence asa congruence sas congruence sss congruence

Question

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

| statement | reason |
| --- | --- |
| $pqrs$ is a rectangle. | given |
|  | interior angles of rectangles are congruent. |
|  | opposite sides of a rectangle are congruent. |
|  | reflexive property |
|  |  |
| $\overline{pr} \cong \overline{qs}$ | corresponding parts of congruent triangles are congruent. |

$\angle psr \cong \angle qrs$ $\angle psr \cong \angle rqp$ $\overline{pq} \cong \overline{rs}$ $\overline{pr} \cong \overline{pr}$ $\overline{ps} \cong \overline{qr}$ $\overline{rs} \cong \overline{sr}$
$\triangle prs \cong \triangle rpq$ $\triangle prs \cong \triangle qsr$
aas congruence asa congruence sas congruence sss congruence

Accepted Answer

# Explanation:
## Step1: State right angles congruence
$\angle PSR \cong \angle RQP$
## Step2: State opposite sides congruence
$\overline{PS} \cong \overline{QR}$
## Step3: State reflexive side congruence
$\overline{RS} \cong \overline{SR}$
## Step4: Prove triangle congruence (SAS)
$	riangle PRS \cong 	riangle RQP$
# Answer:
Filled proof table:
| Statement | Reason |
|-----------|--------|
| $PQRS$ is a rectangle. | Given |
| $\angle PSR \cong \angle RQP$ | Interior angles of rectangles are congruent. |
| $\overline{PS} \cong \overline{QR}$ | Opposite sides of a rectangle are congruent. |
| $\overline{RS} \cong \overline{SR}$ | Reflexive property |
| $	riangle PRS \cong 	riangle RQP$ | SAS congruence |
| $\overline{PR} \cong \overline{QS}$ | Corresponding parts of congruent triangles are congruent. |

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: State right angles congruence

Step2: State opposite sides congruence

Step3: State reflexive side congruence

Step4: Prove triangle congruence (SAS)

Answer:

statement	reason
	interior angles of rectangles are congruent.
	opposite sides of a rectangle are congruent.
	reflexive property

\\(\overline{pr} \cong \overline{qs}\\)	corresponding parts of congruent triangles are congruent.

Statement	Reason
$\angle PSR \cong \angle RQP$	Interior angles of rectangles are congruent.
$\overline{PS} \cong \overline{QR}$	Opposite sides of a rectangle are congruent.
$\overline{RS} \cong \overline{SR}$	Reflexive property
$\triangle PRS \cong \triangle RQP$	SAS congruence
$\overline{PR} \cong \overline{QS}$	Corresponding parts of congruent triangles are congruent.