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In the given proof, we are tasked with proving that triangles \( \Delta UVW \) and \( \Delta UTS \) are congruent using the information provided and completing the missing steps. Here's an analysis of the table:

### Given Information:
- **\( \Delta SUW \) is equilateral**: This means all sides of \( \Delta SUW \) are equal.
- **\( \angle UWV \cong \angle TSU \)**: Given that these two angles are congruent.

### To be filled:
1. **Step 3**: \( \angle VUW \cong \angle SUT \)
   - **Reason**: These angles are congruent because they are vertical angles formed by the intersection of the diagonals \( WV \) and \( TS \).

2. **Step 4**: \( \overline{UW} \cong \overline{SU} \)
   - **Reason**: Since \( \Delta SUW \) is equilateral, all sides are equal, which implies that \( UW = SU \).

### Conclusion:
With the Angle-Side-Angle (ASA) congruence criterion, \( \Delta UVW \cong \Delta UTS \) is proven based on the two pairs of angles and one pair of equal sides.

Do you want further clarification or details on any part of the proof?

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Here are 5 related questions to explore the concept further:
1. What are other congruence criteria apart from ASA?
2. How can you use vertical angles to prove congruence in other triangle problems?
3. What properties of equilateral triangles are most useful in proofs?
4. How do you apply the ASA criterion in non-equilateral triangle problems?
5. Can congruent triangles always guarantee equal area?

**Tip**: When working with geometric proofs, always look for relationships like vertical angles, corresponding sides, and shared angles to establish congruence.

ΔSUW is equilateral. Complete the proof that ΔUVW ≅ ΔUTS.

In this problem, you'll complete the proof that triangles UVW and UTS are congruent using the ASA (Angle-Side-Angle) congruence criterion. You'll apply vertical angles and the properties of equilateral triangles to solve it.

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