From the image provided, the given table lists the statements and reasons for a geometric proof. Here’s how the reasoning for each step can be completed:

1. Statement: $\angle TWU \cong \angle SWT$
   Reason: Definition of congruence (Already provided).

2. Statement: $m\angle SWT + m\angle TWU = 180^\circ$
   Reason: Angles forming a linear pair sum to $180^\circ$ (Already provided).

3. Statement: $m\angle SWT + m\angle TWU = 180^\circ$
   Reason: (Repeated Reason) Angles forming a linear pair sum to $180^\circ$ (Already provided).

4. Statement: $m\angle SWT = 90^\circ$
   Reason: Subtraction property of equality (or, $m\angle TWU = 90^\circ$ due to congruence, and linear pairs split equally).

5. Statement: $\overline{TV} \perp \overline{SU}$
   Reason: Definition of perpendicular lines (Two lines are perpendicular if they form $90^\circ$ angles).

Would you like me to explain any specific part of the reasoning or elaborate further? Here are 5 relative questions to expand on this topic:

1. How does the subtraction property of equality work in geometry proofs?
2. What are linear pairs, and why do they always sum to $180^\circ$?
3. How is the definition of congruence used to justify equal measures of angles?
4. Why does proving one $90^\circ$ angle imply that two lines are perpendicular?
5. How could additional information or diagrams support this proof?

Tip: Always ensure to clearly define key geometric terms in proofs to strengthen your reasoning!