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?