Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point) Responses 10, 20, 15 10, 20, 15 8, 4, 12 8, 4, 12 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.
Therefore, using the given sets of side lengths:
1) 10, 20, 15:
- 10 + 15 > 20 (25 > 20)
- 10 + 20 > 15 (30 > 15)
- 15 + 20 > 10 (35 > 10)
The side lengths 10, 20, and 15 form a triangle.
2) 8, 4, 12:
- 8 + 4 > 12 (12 > 12)
- 8 + 12 > 4 (20 > 4)
- 4 + 12 > 8 (16 > 8)
The side lengths 8, 4, and 12 form a triangle.
3) 8, 8, 20:
- 8 + 8 > 20 (16 > 20)
- 8 + 20 > 8 (28 > 8)
- 8 + 20 > 8 (28 > 8)
The side lengths 8, 8, and 20 do not form a triangle.
4) 20, 10, 30:
- 20 + 10 > 30 (30 > 30)
- 20 + 30 > 10 (50 > 10)
- 10 + 30 > 20 (40 > 20)
The side lengths 20, 10, and 30 form a triangle.