Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point)

Question

Responses

12, 10, 22
12, 10, 22

9, 4, 3
9, 4, 3

2, 7, 6
2, 7, 6

8, 1, 7

Answer 1

To determine which 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.

Let's check each group of side measures:

1. 12, 10, 22
- 12 + 10 = 22 (not greater than 22, so it does not form a triangle)

2. 9, 4, 3
- 9 + 4 > 3
- 9 + 3 > 4
- 4 + 3 > 9
(all these combinations satisfy the Triangle Inequality Theorem, so it forms a triangle)

3. 2, 7, 6
- 2 + 7 > 6
- 2 + 6 > 7
- 7 + 6 > 2
(all these combinations satisfy the Triangle Inequality Theorem, so it forms a triangle)

4. 8, 1, 7
- 8 + 1 > 7
- 8 + 7 > 1
- 1 + 7 > 8
(all these combinations satisfy the Triangle Inequality Theorem, so it forms a triangle)

Therefore, the groups of side measures that will form a triangle are:
- 9, 4, 3
- 2, 7, 6
- 8, 1, 7