Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point) Responses 20, 10, 30 20, 10, 30 8, 8, 20 8, 8, 20 8, 4, 12 8, 4, 12 10, 20, 15...

Answer 1

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 the first set of side lengths:
20 + 10 > 30 (True)
10 + 30 > 20 (True)
20 + 30 > 10 (True)

Therefore, 20, 10, and 30 can form a triangle.

For the second set of side lengths:
8 + 8 > 20 (False)
8 + 20 > 8 (True)
8 + 20 > 8 (True)

Therefore, 8, 8, and 20 cannot form a triangle.

For the third set of side lengths:
8 + 4 > 12 (False)
4 + 12 > 8 (True)
8 + 12 > 4 (True)

Therefore, 8, 4, and 12 cannot form a triangle.

For the fourth set of side lengths:
10 + 20 > 15 (True)
20 + 15 > 10 (True)
10 + 15 > 20 (True)

Therefore, 10, 20, and 15 can form a triangle.