To determine which set of side lengths can form a triangle, we need to apply the Triangle Inequality Theorem. This theorem states that for any three sides to form a triangle, the sum of the lengths of any two sides must be greater than the third side. This must hold true for all combinations of two sides.

Let's go through each option:

1. Side = 15 cm, Side = 7 cm, Side = 7 cm:

   • 15 + 7 = 22 > 7 (True)
   • 7 + 7 = 14 < 15 (False)
   • Since this condition fails, this cannot form a triangle.

2. Side = 15 cm, Side = 7 cm, Side = 9 cm:

   • 15 + 7 = 22 > 9 (True)
   • 15 + 9 = 24 > 7 (True)
   • 7 + 9 = 16 > 15 (True)
   • All conditions are satisfied, so this can form a triangle.

3. Side = 14 cm, Side = 6 cm, Side = 7 cm:

   • 14 + 6 = 20 > 7 (True)
   • 14 + 7 = 21 > 6 (True)
   • 6 + 7 = 13 < 14 (False)
   • This condition fails, so this cannot form a triangle.

4. Side = 14 cm, Side = 6 cm, Side = 8 cm:

   • 14 + 6 = 20 > 8 (True)
   • 14 + 8 = 22 > 6 (True)
   • 6 + 8 = 14 = 14 (False)
   • Since the sum is equal to 14, this cannot form a triangle.

Conclusion:

Only the second option, Side = 15 cm, Side = 7 cm, Side = 9 cm, can form a triangle.

Would you like more details or further explanation on this?

Here are 5 related questions you might find useful:

1. What is the proof of the Triangle Inequality Theorem?
2. How does the Triangle Inequality apply to right triangles?
3. Can a triangle have sides of any length?
4. How do you determine if three angles can form a triangle?
5. What are the different types of triangles based on sides and angles?

Tip: The Triangle Inequality Theorem is crucial in geometry to test whether given side lengths can actually form a valid triangle.