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 8, 1, 7 8, 1, 7 12, 10, 22 12, 10, 22 2, 7, 6

Answer 1

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

Applying this theorem to the given side measures, we can determine which group will form a triangle:

1) 9, 4, 3:
9 + 4 = 13 > 3
9 + 3 = 12 > 4
4 + 3 = 7 > 9

So, the side measures 9, 4, and 3 will form a triangle.

2) 8, 1, 7:
8 + 1 = 9 > 7
8 + 7 = 15 > 1
1 + 7 = 8 > 8

So, the side measures 8, 1, and 7 will form a triangle.

3) 12, 10, 22:
12 + 10 = 22 > 22
12 + 22 = 34 > 10
10 + 22 = 32 > 12

So, the side measures 12, 10, and 22 will form a triangle.

4) 2, 7, 6:
2 + 7 = 9 > 6
2 + 6 = 8 > 7
7 + 6 = 13 > 2

So, the side measures 2, 7, and 6 will form a triangle.

In conclusion, all groups of side measures will form triangles.