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To determine the rule that explains why triangles \( \triangle WVX \) and \( \triangle STU \) are congruent, we examine the information given in the diagram:

1. **Matching Angles**: Both triangles have three pairs of congruent angles. Each angle is marked with matching arcs, showing that:
   - \( \angle W \cong \angle S \)
   - \( \angle V \cong \angle T \)
   - \( \angle X \cong \angle U \)

2. **Congruence Rule**: When two triangles have all corresponding angles congruent, this typically satisfies the **ASA (Angle-Side-Angle)** or **AAS (Angle-Angle-Side)** criteria for congruence, depending on which sides are known. Since no specific sides are marked as congruent here, we only use the angle information provided.

However, since the problem shows no side lengths, it is likely intended to test angle-based congruence criteria. With three pairs of congruent angles, these triangles are **similar** but would need at least one pair of congruent sides to be congruent triangles under AAS or ASA. Thus:

**Correct Answer**: The given answer would be **ASA** if congruent sides are assumed based on symmetry or additional context, otherwise, these triangles may just be similar and **cannot be proven congruent** solely by angles shown.

Would you like further details or have any questions?

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Here are some additional questions to explore this concept further:
1. What is the difference between triangle similarity and congruence?
2. How does the ASA postulate work in determining triangle congruence?
3. When can triangles be congruent with only angle information?
4. What role does the congruence of sides play in triangle congruence rules?
5. Can two triangles with three congruent angles ever fail to be congruent?

**Tip**: Always ensure both angle and side congruence criteria are checked when determining triangle congruence.

Which rule explains why these triangles are congruent? (with options AAS, SAS, SSS, ASA, or 'These triangles cannot be proven congruent')

Determine the rule that explains why two triangles are congruent by analyzing the given congruence conditions. This problem tests knowledge of ASA, AAS, SAS, and SSS congruence theorems in triangle geometry, suitable for students in Grades 8-10.

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