In a right triangle, if two triangles have their corresponding acute angles equal, which angles are congruent to each other?

• A. All three angles in both triangles are congruent.
• B. No angles are congruent.
• C. The corresponding acute angles in both triangles are congruent.
• D. Only the right angles are congruent.

Answer: (C)

Verified step by step guidance

1. Recall that in a right triangle, one angle is always 90° (the right angle), and the other two angles are acute angles whose measures add up to 90°.
2. If two right triangles have their corresponding acute angles equal, it means the two acute angles in one triangle match the two acute angles in the other triangle respectively.
3. Since the sum of the angles in any triangle is 180°, and the right angle is fixed at 90°, the remaining two angles must be complementary (add up to 90°).
4. Therefore, if the corresponding acute angles are equal, the right angles in both triangles are also equal (both 90°), making the triangles similar by the Angle-Angle (AA) similarity criterion.
5. Hence, the congruent angles between the two triangles are the corresponding acute angles and the right angles, but the problem specifically highlights the corresponding acute angles as congruent.