Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point) Responses 8, 4, 12 8, 4, 12 10, 20, 15 10, 20, 15 8, 8, 20 8, 8, 20 20, 10, 30
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.
Let's apply the theorem to each set of side lengths given:
1) 8, 4, 12: 8 + 4 < 12, 8 + 12 > 4, and 4 + 12 > 8
- This set of side lengths forms a triangle.
2) 10, 20, 15: 10 + 20 > 15, 10 + 15 < 20, and 20 + 15 > 10
- This set of side lengths forms a triangle.
3) 8, 8, 20: 8 + 8 > 20, 8 + 20 > 8, and 8 + 20 > 8
- This set of side lengths forms a triangle.
4) 20, 10, 30: 20 + 10 > 30, 20 + 30 > 10, and 10 + 30 > 20
- This set of side lengths forms a triangle.
Based on the applications of the Triangle Inequality Theorem, all four sets of side lengths form triangles.