Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point) Responses 2, 7, 6 2, 7, 6 12, 10, 22 12, 10, 22 9, 4, 3 9, 4, 3 8, 1, 7
To determine which group of side measures will form a triangle, we can apply the Triangle Inequality Theorem, which 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 analyze each group of side measures:
1) 2, 7, 6: To form a triangle, the sum of any two sides must be greater than the third side.
- 2 + 7 = 9 > 6
- 2 + 6 = 8 > 7
- 7 + 6 = 13 > 2
Therefore, the group of side measures 2, 7, 6 will form a triangle.
2) 12, 10, 22: Applying the Triangle Inequality Theorem:
- 12 + 10 = 22 > 22
- 12 + 22 = 34 > 10
- 10 + 22 = 32 > 12
Therefore, the group of side measures 12, 10, 22 will form a triangle.
3) 9, 4, 3: Applying the Triangle Inequality Theorem:
- 9 + 4 = 13 > 3
- 9 + 3 = 12 > 4
- 4 + 3 = 7 > 9
Therefore, the group of side measures 9, 4, 3 will NOT form a triangle.
4) 8, 1, 7: Applying the Triangle Inequality Theorem:
- 8 + 1 = 9 > 7
- 8 + 7 = 15 > 1
- 1 + 7 = 8 > 8
Therefore, the group of side measures 8, 1, 7 will form a triangle.
In conclusion, the groups of side measures that will form a triangle are 2, 7, 6 and 12, 10, 22.