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To construct a triangle from three given segments, the sum of the lengths of any two sides must be greater than the length of the third side. Let's analyze each option: 1. **9 cm, 18 cm, 15 cm** - 9 + 15 > 18 (24 > 18) ✔️ - 9 + 18 > 15 (27 > 15) ✔️ - 15 + 18 > 9 (33 > 9) ✔️ - Possible 2. **21.5 cm, 5.5 cm, 15 cm** - 5.5 + 15 = 20.5, not greater than 21.5 ✖️ - Not possible 3. **18.5 cm, 25.5 cm, 39.5 cm** - 18.5 + 25.5 > 39.5 (44 > 39.5) ✔️ - 18.5 + 39.5 > 25.5 (58 > 25.5) ✔️ - 25.5 + 39.5 > 18.5 (65 > 18.5) ✔️ - Possible 4. **29.5 cm, 0.5 cm, 30.5 cm** - 0.5 + 29.5 > 30.5 ✖️ (30 = 30.5) - Not possible 5. **5 cm, 5 cm, 11 cm** - 5 + 5 = 10, not greater than 11 ✖️ - Not possible 6. **6.5 cm, 9 cm, 3 cm** - 3 + 6.5 = 9.5, greater than 9 ✔️ - 3 + 9 > 6.5 (12 > 6.5) ✔️ - 6.5 + 9 > 3 (15.5 > 3) ✔️ - Possible 7. **16 cm, 10 cm, 32 cm** - 10 + 16 = 26, not greater than 32 ✖️ - Not possible The possible combinations are: - 9 cm, 18 cm, 15 cm - 18.5 cm, 25.5 cm, 39.5 cm - 6.5 cm, 9 cm, 3 cm