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
2, 7, 6
2, 7, 6
8, 1, 7
8, 1, 7
9, 4, 3
To determine if a triangle can be formed using the Triangle Inequality Theorem, we need to check if the sum of the lengths of any two sides is greater than the length of the third side.
1. For the measurements 12, 10, and 22:
- 12 + 10 = 22, which is NOT greater than 22.
- 10 + 22 = 32, which IS greater than 12.
- 12 + 22 = 34, which IS greater than 10.
Therefore, the measurements 12, 10, and 22 will form a triangle.
2. For the measurements 2, 7, and 6:
- 2 + 7 = 9, which IS greater than 6.
- 7 + 6 = 13, which IS greater than 2.
- 2 + 6 = 8, which IS greater than 7.
Therefore, the measurements 2, 7, and 6 will form a triangle.
3. For the measurements 8, 1, and 7:
- 8 + 1 = 9, which IS greater than 7.
- 1 + 7 = 8, which IS greater than 8.
- 8 + 7 = 15, which IS greater than 1.
Therefore, the measurements 8, 1, and 7 will form a triangle.
4. For the measurements 9, 4, and 3:
- 9 + 4 = 13, which IS greater than 3.
- 4 + 3 = 7, which IS greater than 9.
- 9 + 3 = 12, which IS greater than 4.
Therefore, the measurements 9, 4, and 3 will form a triangle.
So, the groups of side measures that will form a triangle are:
- 12, 10, 22
- 2, 7, 6
- 8, 1, 7
- 9, 4, 3