Question

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

2, 7, 6
2, 7, 6

12, 10, 22

Answer 1

wrong

Answer 2

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

In the given options:

1) 9 + 4 = 13 > 3
9 + 3 = 12 > 4
4 + 3 = 7 > 9
Therefore, the group of side measures 9, 4, and 3 will form a triangle.

2) 8 + 1 = 9 > 7
8 + 7 = 15 > 1
1 + 7 = 8 ≤ 8
Therefore, the group of side measures 8, 1, and 7 will not form a triangle.

3) 2 + 7 = 9 > 6
2 + 6 = 8 > 7
7 + 6 = 13 > 2
Therefore, the group of side measures 2, 7, and 6 will form a triangle.

4) 12 + 10 = 22 > 22
12 + 22 = 34 > 10
10 + 22 = 32 > 12
Therefore, the group of side measures 12, 10, and 22 will form a triangle.

Answer 3

I apologize for the mistake. Let's reassess the options using the Triangle Inequality Theorem:

1) 9 + 4 = 13 > 3
9 + 3 = 12 > 4
4 + 3 = 7 > 9
Therefore, the group of side measures 9, 4, and 3 will form a triangle.

2) 8 + 1 = 9 > 7
8 + 7 = 15 > 1
1 + 7 = 8 > 8
Therefore, the group of side measures 8, 1, and 7 will form a triangle.

3) 2 + 7 = 9 > 6
2 + 6 = 8 > 7
7 + 6 = 13 > 2
Therefore, the group of side measures 2, 7, and 6 will form a triangle.

4) 12 + 10 = 22 > 22
12 + 22 = 34 > 10
10 + 22 = 32 > 12
Therefore, the group of side measures 12, 10, and 22 will form a triangle.

Apologies for the confusion in my initial response. In this case, all four groups of side measures will form triangles.