* Which set of line segments can be used to construct a triangle? A 6 cm, 2 cm, and 9 cm B 8 cm, 2 cm, and 5 cm C 8 cm, 3 cm, and 3 cm D 6 cm, 5 cm, and 2 cm

To determine which set of line segments can form a triangle, we can apply the **Triangle Inequality Theorem**. This theorem states that the sum of the lengths of any two sides of a triangle must be **greater than the length of the third side**.

We will check each option:

1. **Option A: 6 cm, 2 cm, and 9 cm**
   - \(6 + 2 = 8\) (which is **less** than 9), so these lengths **cannot** form a triangle.
   
2. **Option B: 8 cm, 2 cm, and 5 cm**
   - \(8 + 2 = 10\) (which is **greater** than 5),
   - \(8 + 5 = 13\) (which is **greater** than 2),
   - \(5 + 2 = 7\) (which is **less** than 8), so these lengths **cannot** form a triangle.
   
3. **Option C: 8 cm, 3 cm, and 3 cm**
   - \(8 + 3 = 11\) (which is **greater** than 3),
   - \(8 + 3 = 11\) (which is **greater** than 3),
   - \(3 + 3 = 6\) (which is **less** than 8), so these lengths **cannot** form a triangle.
   
4. **Option D: 6 cm, 5 cm, and 2 cm**
   - \(6 + 5 = 11\) (which is **greater** than 2),
   - \(6 + 2 = 8\) (which is **greater** than 5),
   - \(5 + 2 = 7\) (which is **greater** than 6), so these lengths **can** form a triangle.

### Conclusion:
The set of line segments that can be used to construct a triangle is **Option D: 6 cm, 5 cm, and 2 cm**.

Would you like further details or explanations?

Here are 5 related questions to think about:
1. How does the Triangle Inequality Theorem apply to right triangles?
2.

Which set of line segments can be used to construct a triangle? A 6 cm, 2 cm, and 9 cm B 8 cm, 2 cm, and 5 cm C 8 cm, 3 cm, and 3 cm D 6 cm, 5 cm, and 2 cm

Learn how to determine if sets of line segments can form a triangle using the Triangle Inequality Theorem. Explore the problem of which set of line segments—6 cm, 2 cm, and 9 cm; 8 cm, 2 cm, and 5 cm; 8 cm, 3 cm, and 3 cm; or 6 cm, 5 cm, and 2 cm—can construct a valid triangle. This problem is suitable for Grades 6-8 students.

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