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

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.

1. For the first set of side lengths: 10, 20, 15
10 + 15 = 25 > 20 (True)
10 + 20 = 30 > 15 (True)
15 + 20 = 35 > 10 (True)
All three conditions are met, so 10, 20, 15 can form a triangle.

2. For the second set of side lengths: 20, 10, 30
20 + 30 = 50 > 10 (True)
20 + 10 = 30 > 30 (False)
10 + 30 = 40 > 20 (True)
Not all conditions are met, so 20, 10, 30 cannot form a triangle.

3. For the third set of side lengths: 8, 4, 12
8 + 12 = 20 > 4 (True)
8 + 4 = 12 > 12 (False)
4 + 12 = 16 > 8 (True)
Not all conditions are met, so 8, 4, 12 cannot form a triangle.

4. For the fourth set of side lengths: 8, 8, 20
8 + 20 = 28 > 8 (True)
8 + 8 = 16 > 20 (False)
8 + 20 = 28 > 8 (True)
Not all conditions are met, so 8, 8, 20 cannot form a triangle.

Therefore, only 10, 20, 15 form a triangle.