Final answer:
Options B (5 m, 7 m, 12 m) and C (6 cm, 12 cm, 17 cm) can form a triangle because in each case, the sum of any two sides is greater than the length of the third side, satisfying the Triangle Inequality Theorem.
Step-by-step explanation:
To determine which groups of line segment lengths could form a triangle, we apply the Triangle Inequality Theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
- A. 2 in, 3 in, 8 in. - This set cannot form a triangle because 2 + 3 is not greater than 8.
- B. 5 m, 7 m, 12 m - This set can form a triangle because each pair of sides sums to a value greater than the third side (5+7>12, 5+12>7, and 7+12>5).
- C. 6 cm, 12 cm, 17 cm - This set can form a triangle because each pair of sides sums to a value greater than the third side (6+12>17, 6+17>12, and 12+17>6).
- D. 4 ft, 4 ft, 8 ft - This set cannot form a triangle because 4 + 4 is not greater than 8.
Based on these evaluations, options B and C could form a triangle, whereas options A and D could not.