To prove $\triangle PQR \cong \triangle PSR$ using the given information, let's go step by step and fill in the missing reasons in the proof.

Given:

1. $\overline{QR} \cong \overline{SR}$ (Given)
2. $\overline{PQ} \cong \overline{PS}$ (Given)
3. $\overline{PR} \cong \overline{PR}$ (Reflexive Property)

Proof:

Using the SSS (Side-Side-Side) Congruence Postulate, if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

1. Statement: $\overline{QR} \cong \overline{SR}$
   Reason: Given

2. Statement: $\overline{PQ} \cong \overline{PS}$
   Reason: Given

3. Statement: $\overline{PR} \cong \overline{PR}$
   Reason: Reflexive Property

4. Statement: $\triangle PQR \cong \triangle PSR$
   Reason: SSS Congruence Postulate

Completed Proof:

The triangles are congruent based on the SSS Congruence Postulate since all three pairs of corresponding sides are congruent.

Do you have any questions about this solution? Would you like me to break it down further? Here are some related questions:

1. What is the difference between the SSS and SAS Congruence Postulates?
2. How does the Reflexive Property apply in this proof?
3. What are the conditions for using the SSS Postulate?
4. Can this proof be completed using SAS instead of SSS?
5. How can congruence be used to prove similarity in triangles?

Tip: Always identify all congruent sides or angles before choosing a congruence postulate. This simplifies the proof process!