Final answer:
To determine which set of side lengths will not form a triangle, we need to apply the Triangle Inequality Theorem. The sets of side lengths that will not form a triangle are 10 in., 13 in., 18 in. and 8.5 in., 12.5 in., 16.5 in.
Step-by-step explanation:
To determine which set of side lengths will not form a triangle, we need to apply the Triangle Inequality Theorem.
The 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.
Let's apply this theorem to each set of side lengths:
10 in., 13 in., 18 in.: 10 + 13 = 23, which is less than 18. Therefore, this set will NOT form a triangle.
6 in., 10 in., 10 in.: 6 + 10 = 16, which is equal to 10 but less than 10 + 10 = 20. Therefore, this set will form a triangle.
4.5 in., 6.5 in., 11 in.: 4.5 + 6.5 = 11, which is equal to 11 but less than 11 + 11 = 22. Therefore, this set will form a triangle.
8.5 in., 12.5 in., 16.5 in.: 8.5 + 12.5 = 21, which is less than 16.5. Therefore, this set will NOT form a triangle.
Based on the Triangle Inequality Theorem, the sets of side lengths that will not form a triangle are 10 in., 13 in., 18 in. and 8.5 in., 12.5 in., 16.5 in.