This image shows a two-column geometric proof with "Statements" on the left and "Reasons" on the right.

Here’s a breakdown of the missing parts:

• Statement 3: $m\angle U + m\angle S = 90^\circ$ Reason: "Definition of complementary angles" (This follows from the given fact that angles $U$ and $S$ are complementary).

• Statement 7: $\angle T \cong \angle U$ Reason: "Definition of congruent angles" (Two angles are congruent if they have the same measure, which was proven in step 6 where $m\angle T = m\angle U$).

Would you like further details or clarification on any step?

Here are 5 related questions to expand on the topic:

1. What does it mean for two angles to be complementary?
2. How do you apply the Transitive Property of Equality in geometric proofs?
3. Why is the "definition of congruent angles" used in the last step of the proof?
4. Can complementary angles be congruent? Why or why not?
5. How would you apply this proof to different angle pairs?

Tip: When proving angles are congruent, always look for relationships between their measures, such as equality or being supplementary/complementary.