Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point) Responses 8, 8, 20 10, 20, 15 20, 10, 30 8, 4, 12
To apply the Triangle Inequality Theorem, we need to check if the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Testing each given set of side lengths:
1) 8, 8, 20
The sum of the lengths of the first two sides is 8 + 8 = 16, which is less than the length of the third side (20). Therefore, the lengths 8, 8, and 20 do not form a triangle.
2) 10, 20, 15
The sum of the lengths of the first two sides is 10 + 20 = 30, which is greater than the length of the third side (15). Also, the sum of the lengths of the second and third sides is 20 + 15 = 35, which is greater than the length of the first side (10). Finally, the sum of the lengths of the first and third sides is 10 + 15 = 25, which is greater than the length of the second side (20). Therefore, the lengths 10, 20, and 15 do form a triangle.
3) 20, 10, 30
The sum of the lengths of the first two sides is 20 + 10 = 30, which is equal to the length of the third side (30). Therefore, the lengths 20, 10, and 30 do not form a triangle because the sum of the lengths of two sides must be greater than the length of the third side, not equal to it.
4) 8, 4, 12
The sum of the lengths of the first two sides is 8 + 4 = 12, which is equal to the length of the third side (12). Therefore, the lengths 8, 4, and 12 do not form a triangle because the sum of the lengths of two sides must be greater than the length of the third side, not equal to it.
In conclusion, only the lengths 10, 20, and 15 form a triangle.