Question

statements reasons
$overline{pq}congoverline{sr}$ given
$angle pqrcongangle srq$ given
$overline{qr}congoverline{qr}$ x
$\triangle pqrcong\triangle srq$ y

Explanation:

Step1: Identify reason for $\overline{QR}\cong\overline{QR}$

The segment $\overline{QR}$ is congruent to itself by the reflexive property of congruence which states that any geometric figure is congruent to itself.

Step2: Identify reason for $\triangle PQR\cong\triangle SRQ$

We are given $\overline{PQ}\cong\overline{SR}$, $\angle PQR\cong\angle SRQ$, and $\overline{QR}\cong\overline{QR}$. By the Side - Angle - Side (SAS) congruence postulate, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. Here, $\overline{PQ}$ and $\overline{SR}$ are sides, $\angle PQR$ and $\angle SRQ$ are the included angles, and $\overline{QR}$ is the common side.

Answer:

[x] Reflexive Property of Congruence
[y] Side - Angle - Side (SAS) Congruence Postulate