1. The problem asks if the given sets of side lengths can form a triangle. 2. Recall the triangle inequality theorem: For any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. Check each set: 3. Set 1: 5, 7, 10 - 5 + 7 = 12 > 10 ✓ - 7 + 10 = 17 > 5 ✓ - 5 + 10 = 15 > 7 ✓ All conditions met, so YES. 4. Set 2: 4, 4, 9 - 4 + 4 = 8 < 9 ✗ Fails the condition, so NO. 5. Set 3: 8, 3, 4 - 8 + 3 = 11 > 4 ✓ - 3 + 4 = 7 < 8 ✗ Fails, so NO. 6. Set 4: 6, 6, 6 - 6 + 6 = 12 > 6 ✓ (true for all sides since equal) All conditions met, so YES. 7. Set 5: 12, 7, 5 - 12 + 7 = 19 > 5 ✓ - 7 + 5 = 12 = 12 ✗ (sum must be strictly greater than the third side) - 12 + 5 = 17 > 7 ✓ Fails, so NO. Final Answers: 1. YES 2. NO 3. NO 4. YES 5. NO