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To complete the proof that \( \triangle PRS \cong \triangle PQS \), we need to complete Statements 4 and 5 in the given table. Here’s the reasoning for each:

### Steps:
1. **Statement 4**: \( PS \cong PS \)
   - **Reason**: This is based on the **Reflexive Property** of congruence, as any segment is congruent to itself.

2. **Statement 5**: \( \triangle PRS \cong \triangle PQS \)
   - **Reason**: By the **SAS (Side-Angle-Side) Congruence Postulate**. We have:
     - \( \angle QPS \cong \angle RPS \) (from Statement 3),
     - \( PQ \cong PR \) (from Statement 2), and
     - \( PS \cong PS \) (from Statement 4).

So, the completed table should look like this:

| Statement                     | Reason                             |
|-------------------------------|------------------------------------|
| 1. \( PS \) bisects \( \angle QPR \)    | Given                              |
| 2. \( PQ \cong PR \)                   | Given                              |
| 3. \( \angle QPS \cong \angle RPS \)   | Definition of angle bisector       |
| 4. \( PS \cong PS \)                   | Reflexive Property                 |
| 5. \( \triangle PRS \cong \triangle PQS \) | SAS Congruence Postulate           |

Would you like a more detailed explanation, or do you have any specific questions?

### Related Questions:
1. What is the SAS Congruence Postulate, and why is it used here?
2. How does the Reflexive Property help in proving congruence?
3. What role does an angle bisector play in congruent triangle proofs?
4. Can the ASA (Angle-Side-Angle) postulate also be used for this proof? Why or why not?
5. Why is it important to state congruence properties when proving triangles congruent?

### Tip:
When proving triangles congruent, always ensure you have identified at least three congruent parts (sides or angles) that match one of the congruence postulates: SSS, SAS, ASA, or AAS.

PS bisects ∠QPR and PQ ≅ PR. Complete the proof that △PRS ≅ △PQS.

Learn how to complete the proof that △PRS ≅ △PQS given that PS bisects ∠QPR and PQ ≅ PR. This problem involves concepts such as triangle congruence using the SAS postulate and the Reflexive Property. Suitable for students in Grades 8-10.

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