Question

Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point) Responses 8, 1, 7 8, 1, 7 2, 7, 6 2, 7, 6 9, 4, 3 9, 4, 3 12, 10, 22

Answer 1

You have to pick one

Answer 2

The Triangle Inequality Theorem 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 apply this theorem to each group of side measures:

1) 8, 1, 7
8 + 1 > 7 (True)
8 + 7 > 1 (True)
1 + 7 > 8 (True)
These side measures will form a triangle.

2) 2, 7, 6
2 + 7 > 6 (True)
2 + 6 > 7 (True)
7 + 6 > 2 (True)
These side measures will form a triangle.

3) 9, 4, 3
9 + 4 > 3 (True)
9 + 3 > 4 (True)
4 + 3 > 9 (False)
These side measures will NOT form a triangle.

4) 12, 10, 22
12 + 10 > 22 (False)
12 + 22 > 10 (True)
10 + 22 > 12 (True)
These side measures will NOT form a triangle.

So, the groups that will form a triangle are:
1) 8, 1, 7
2) 2, 7, 6