The proof seems almost complete. The goal is to prove that ∠T ≅ ∠S. Let's walk through it:

Statements and Reasons:

1. ∠R and ∠S are complementary
   Reason: Given.

2. ∠T and ∠R are complementary
   Reason: Given.

3. m∠R + m∠S = 90°
   Reason: Definition of complementary angles.

4. m∠T + m∠R = 90°
   Reason: Definition of complementary angles.

5. m∠R + m∠S = m∠T + m∠R
   Reason: Transitive Property of Equality (both sums equal 90°).

6. m∠T = m∠S
   Reason: Properties of addition, subtraction, multiplication, and division (subtracting m∠R from both sides).

Missing step:

7. ∠T ≅ ∠S
   Reason: Definition of congruent angles (if their measures are equal, the angles are congruent).

Would you like more details or have any questions?

Here are 5 related questions to explore this topic further:

1. How can you prove angles are congruent using other geometric theorems?
2. What are some common properties of complementary angles in geometry?
3. Can this proof be extended to non-right triangles? Why or why not?
4. How does the Transitive Property of Equality apply in geometric proofs?
5. How would the proof change if the angles were supplementary instead of complementary?

Tip:

When proving angles congruent, always remember that the equality of their measures is the key criterion.