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The image you provided appears to show a geometry proof problem involving congruent angles. Here is the problem breakdown and what can be deduced from it:

### Given:
- \(\angle RSU \cong \angle VST\)

### Prove:
- \(\angle RSV \cong \angle UST\)

### Statements and Reasons (Partial Proof):

| Step | Statements                                             | Reasons          |
|------|--------------------------------------------------------|------------------|
| 1    | \(\angle RSU \cong \angle VST\)                        | Given            |
| 2    | \(m\angle RSU = m\angle VST\)                          | Definition of congruent angles |
| 3    | \(m\angle RSU + m\angle USV = m\angle RSV\)            | Angle addition postulate |
| 4    | \(m\angle VST + m\angle USV = m\angle UST\)            | Angle addition postulate |
| 5    | \(m\angle RSV = m\angle UST\)                          | Substitution |
| 6    | \(\angle RSV \cong \angle UST\)                        | Definition of congruent angles |

- The reason for Step 1 is "Given" (as already noted).
- The reason for Step 2 is based on the **definition of congruent angles**.
- The reasoning in Step 3 and Step 4 comes from the **angle addition postulate**, which states that if you add two adjacent angles, the result is the measure of the entire angle.
- For Step 5, we use **substitution**, as both angles \(m\angle RSU + m\angle USV\) and \(m\angle VST + m\angle USV\) are equal by the earlier steps.
- The final step is using the **definition of congruent angles** again.

This proof shows the flow from the given information to the final conclusion using properties of angles and congruence.

Would you like more details on any specific steps? 

Here are 5 related questions to expand on the concept:
1. What is the angle addition postulate, and how is it applied?
2. What other properties can be used to prove congruent angles in a triangle?
3. How does substitution work in geometric proofs?
4. Why is the definition of congruent angles crucial in this proof?
5. Can you apply the transitive property of congruence in this proof?

**Tip:** Always look for angles or sides that are shared or congruent between figures, as they often serve as the key to completing a geometric proof.

Given that angle RSU is congruent to angle VST, prove that angle RSV is congruent to angle UST.

Explore how to prove that angles RSV and UST are congruent based on the given condition that angle RSU is congruent to angle VST. This step-by-step geometry proof uses the angle addition postulate, the definition of congruent angles, and substitution properties. Ideal for students in Grades 9-10.

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