Question

use the given information to prove that △pqr≅△rsp. given: $overline{pq}=overline{rs}$, $overline{qr}=overline{sp}$. prove: △pqr = △rsp. statement reason 1 $overline{pq}=overline{rs}$ reason? 2 $overline{qr}=overline{sp}$ given 3 $overline{pr}=overline{pr}$ reason? 4 △pqr = △rsp reason?

Explanation:

Step1: State given side - equality

Given $\overline{PQ}=\overline{RS}$.

Step2: State other given side - equality

Given $\overline{QR}=\overline{SP}$.

Step3: Identify common side

$\overline{PR}=\overline{PR}$ by the reflexive property of congruence (any segment is congruent to itself).

Step4: Apply congruence criterion

By the Side - Side - Side (SSS) congruence criterion, if three sides of one triangle are congruent to three sides of another triangle, the two triangles are congruent. So, $\triangle PQR\cong\triangle RSP$.

Answer:

1. Reason: Given
2. $\overline{SP}$
3. Reason: Reflexive property of congruence
4. Reason: SSS (Side - Side - Side) congruence criterion