Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point) Responses 9, 4, 3 9, 4, 3 2, 7, 6 2, 7, 6 12, 10, 22 12, 10, 22 8, 1, 7
To determine if a group of side measures will form a triangle, we need to 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.
For response 9, 4, 3:
9 + 4 > 3
9 + 3 > 4
4 + 3 > 9
The sum of the lengths of any two sides is greater than the length of the third side. Therefore, this group of side measures will form a triangle.
For response 2, 7, 6:
2 + 7 > 6
2 + 6 > 7
7 + 6 > 2
The sum of the lengths of any two sides is greater than the length of the third side. Therefore, this group of side measures will form a triangle.
For response 12, 10, 22:
12 + 10 > 22
12 + 22 > 10
10 + 22 > 12
The sum of the lengths of any two sides is not greater than the length of the third side. Therefore, this group of side measures will not form a triangle.
For response 8, 1, 7:
8 + 1 > 7
8 + 7 > 1
1 + 7 > 8
The sum of the lengths of any two sides is greater than the length of the third side. Therefore, this group of side measures will form a triangle.
So, the groups of side measures that will form a triangle are: 9, 4, 3 and 8, 1, 7.