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