1. **Problem Statement:** Given that angles PTQ and STR are vertical angles and congruent, we need to determine which chords in the circle are congruent. 2. **Key Concept:** Vertical angles are equal in measure. When two chords intersect inside a circle, the vertical angles formed are congruent, and the chords opposite these angles are also congruent. 3. **Identify the chords:** The chords mentioned are QP, SR, QR, PQ, PR, RS, and PS. 4. **Analyze the vertical angles:** Angles PTQ and STR are vertical angles formed by the intersection of chords PR and QS at point T. 5. **Conclusion:** Since vertical angles PTQ and STR are congruent, the chords that form these angles and are opposite each other are congruent. These chords are PR and QS. 6. **Answer:** The congruent chords are PR and QS. Note: The options given do not list QS explicitly, but PR and PS are listed. Since PS is not opposite PR, the correct pair is PR and SR (assuming SR corresponds to QS). Given the options, the closest correct answer is **PR and SR**.