1. **Problem Statement:** Given four triangles Q, R, S, and T with angles and side lengths as follows: - Triangle Q: angles 65°, 45°, and one unknown; side length 10 opposite 65°. - Triangle R: angles 45°, 60°, and one unknown; side length 10 opposite 60°. - Triangle S: angles 70°, 45°, and one unknown; side length 10 opposite 70°. - Triangle T: angles 65°, 45°, and one unknown; side length 10 opposite 65°. Determine which two triangles are congruent. 2. **Recall Congruence Criteria:** Triangles are congruent if they have exactly the same size and shape, which can be established by criteria such as SAS (Side-Angle-Side), ASA (Angle-Side-Angle), or SSS (Side-Side-Side). 3. **Analyze Triangles Q and T:** - Both have angles 65° and 45°. - Both have a side length of 10 opposite the 65° angle. - The third angle in each triangle is $180^\circ - 65^\circ - 45^\circ = 70^\circ$. 4. **Check Corresponding Parts:** - Triangle Q angles: 65°, 45°, 70°. - Triangle T angles: 65°, 45°, 70°. - Side length 10 opposite 65° in both. 5. **Conclusion:** Triangles Q and T have the same angles and corresponding side lengths, so they are congruent by ASA (Angle-Side-Angle) criterion. **Final answer:** Triangles Q and T are congruent.