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To solve this problem, we need to identify which triangle in the options is a right triangle. A right triangle is a triangle in which one of the angles is exactly 90°.

### Steps to Determine the Right Triangle:

1. **Check the Pythagorean Theorem**: The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides:
   
   \[
   c^2 = a^2 + b^2
   \]

2. **Apply the Pythagorean Theorem** to each of the given triangles to determine if any of them satisfies the equation.

### Analyzing Each Triangle:
- **Triangle A**:
  - Sides: 13, 12, 5
  - Check: \( 13^2 = 12^2 + 5^2 \)
  - \( 169 = 144 + 25 \)
  - \( 169 = 169 \) (This is a right triangle)
  
- **Triangle B**:
  - Sides: 8, 15, 17
  - Check: \( 17^2 = 15^2 + 8^2 \)
  - \( 289 = 225 + 64 \)
  - \( 289 = 289 \) (This is also a right triangle)

- **Triangle C**:
  - Sides: 7, 24, 25
  - Check: \( 25^2 = 24^2 + 7^2 \)
  - \( 625 = 576 + 49 \)
  - \( 625 = 625 \) (This is another right triangle)

- **Triangle D**:
  - Sides: 10, 6, 8
  - Check: \( 10^2 = 8^2 + 6^2 \)
  - \( 100 = 64 + 36 \)
  - \( 100 = 100 \) (This is a right triangle as well)

### Conclusion:
- All triangles listed (A, B, C, D) satisfy the Pythagorean Theorem and are thus right triangles. The correct answer is **all of the above triangles** are right triangles.

### Would you like more details or have any questions?

Here are five related questions that might interest you:
1. How do you determine if a triangle is a right triangle using angles?
2. What are some real-world applications of the Pythagorean Theorem?
3. How does the converse of the Pythagorean Theorem work?
4. What is the importance of special right triangles in geometry?
5. How can you use trigonometric ratios to solve right triangles?

**Tip**: In problems like these, always double-check your calculations to ensure the correct application of the Pythagorean Theorem.

Which triangle is labeled as a right triangle?

Determine which triangle is labeled as a right triangle using the Pythagorean Theorem. Analyze the side lengths of each triangle and apply the formula c^2 = a^2 + b^2 to verify the results. Suitable for students in Grades 7-9.

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