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In this problem, we are asked to determine which congruence rule can be used to prove that the triangles \( \triangle PQR \) and \( \triangle TUS \) are congruent.

### Observing the triangles:

- \( \triangle PQR \) and \( \triangle TUS \) are both right-angled triangles as indicated by the square markings at \( \angle Q \) and \( \angle U \).
- Both triangles have the right angle.
- The hypotenuses \( PR \) and \( TS \) are marked as congruent.
- The legs \( PQ \) and \( TU \) are also marked as congruent.

### Conclusion:
The triangles are congruent by **RHS (Right angle-Hypotenuse-Side)** congruence rule, because:
1. Both triangles have a right angle.
2. The hypotenuses are equal.
3. One of the legs is also equal.

Thus, the correct answer is:
\[ \boxed{\text{ } \triangle PQR \cong \triangle TUS \text{ by RHS congruence rule} } \]

Let me know if you'd like further clarification or details!

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Here are 5 related questions to expand your understanding:

1. What are the conditions for two triangles to be congruent by the RHS rule?
2. How is the RHS rule different from the SAS rule?
3. Can two right triangles be congruent if only one pair of legs is equal but the hypotenuses differ?
4. In what situations would the AAS rule be used instead of the RHS rule?
5. Why is the hypotenuse the longest side in a right triangle?

**Tip:** In triangle congruence, always check for matching sides and angles between the triangles to apply the correct congruence rule (SAS, AAS, RHS, etc.).

Which of the following statements is true? 
1. ΔPQR ≅ ΔTUS by ASA congruence rule 
2. ΔPQR ≅ ΔTUS by AAS congruence rule 
3. ΔPQR ≅ ΔTUS by RHS congruence rule 
4. ΔPQR ≅ ΔTUS by SAS congruence rule

Learn how to determine the congruence of triangles using different rules such as RHS, ASA, AAS, and SAS. Understand the application of each congruence rule to solve problems related to triangle properties. Suitable for Grades 8-10.

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