apply the triangle inequality theorem to determine which three side lengths form a triangle

Answer 1

To determine which three side lengths form a triangle, we need to apply the triangle inequality theorem.

The triangle inequality 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.

For example, if we have side lengths of 4, 5, and 9:

1. 4 + 5 = 9 (valid)
2. 5 + 9 = 14 (valid)
3. 4 + 9 = 13 (valid)

Since all three combinations of side lengths satisfy the triangle inequality theorem, sides of length 4, 5, and 9 can form a triangle.