Question

Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point)
Responses

12, 10, 22
12, 10, 22

2, 7, 6
2, 7, 6

9, 4, 3
9, 4, 3

8, 1, 7

Answer 1

Which one is it?

Answer 2

According to the Triangle Inequality Theorem, for a triangle to be formed, the sum of the lengths of any two sides of the triangle must be greater than the length of the third side.

Analyzing the given groups of side measures:

1) 12, 10, 22: To determine if a triangle can be formed using these side measures, we check if the sum of any two sides is greater than the third side.
- 22 + 10 = 32, which is greater than 12.
- 12 + 22 = 34, which is greater than 10.
- 12 + 10 = 22, which is not greater than 22.
Therefore, a triangle cannot be formed with side measures 12, 10, 22.

2) 2, 7, 6:
- 2 + 7 = 9, which is greater than 6.
- 7 + 6 = 13, which is greater than 2.
- 2 + 6 = 8, which is greater than 7.
Therefore, a triangle can be formed with side measures 2, 7, 6.

3) 9, 4, 3:
- 9 + 4 = 13, which is greater than 3.
- 4 + 3 = 7, which is greater than 9.
- 9 + 3 = 12, which is greater than 4.
Therefore, a triangle can be formed with side measures 9, 4, 3.

4) 8, 1, 7:
- 8 + 1 = 9, which is greater than 7.
- 1 + 7 = 8, which is not greater than 8.
- 8 + 7 = 15, which is greater than 1.
Therefore, a triangle cannot be formed with side measures 8, 1, 7.

Only group 2) and group 3) have side measures that form a triangle.

Answer 3

Based on the analysis, the group of side measures that will form a triangle is group 2) with side measures 2, 7, and 6.