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In the image, four pairs of similar triangles are shown. To determine the correct similarity statement for the fourth pair of triangles (Triangle \( TUV \) and Triangle \( PQR \)):

### Step-by-Step Analysis:

1. **Angle Matching**: 
   - For triangle \( TUV \): 
     - \( \angle T = 85^\circ \)
     - \( \angle V = 66^\circ \)
     - \( \angle U = 29^\circ \) (because the sum of angles in a triangle is \( 180^\circ \))

   - For triangle \( PQR \): 
     - \( \angle P = 85^\circ \)
     - \( \angle R = 66^\circ \)
     - \( \angle Q = 29^\circ \) (similarly from triangle angle sum property)

2. **Corresponding Angles**:
   Since the angles are the same, the triangles are similar by the **AA (Angle-Angle) Similarity** criterion. Now, we need to match the corresponding vertices:

   - \( \angle T \) corresponds to \( \angle P \) (both are \( 85^\circ \)),
   - \( \angle U \) corresponds to \( \angle Q \) (both are \( 29^\circ \)),
   - \( \angle V \) corresponds to \( \angle R \) (both are \( 66^\circ \)).

### Conclusion:

The correct similarity statement is **Triangle \( TUV \sim Triangle PQR \)**, since the vertices match based on corresponding angles.

### Do you need more details or further clarifications? Here are 5 related questions you could explore:

1. What is the AA similarity criterion in triangles?
2. How can you prove that two triangles are similar using side ratios?
3. Can two triangles be similar if they share only one equal angle?
4. What are the other criteria for triangle similarity besides AA?
5. How do you solve for unknown sides using triangle similarity?

**Tip:** Remember that corresponding angles in similar triangles always match, and their sides are proportional.

Based on the triangles shown, which similarity statement about the fourth pair of triangles is true and can be used to complete the table?

Learn how to determine the correct similarity statement for a pair of triangles using the AA (Angle-Angle) similarity theorem. This problem involves analyzing the angles in two triangles and matching corresponding angles. Suitable for students in Grades 8-10.

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