Apply the triangle inequality THEOREM and determine which group of side measures will form a triangle
8,1,7
12, 10, 22
2,7,6
9,4,3
To determine which group of side measures will form a triangle, we need to apply the triangle inequality theorem.
The theorem states that in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
1. For the group of side measures: 8, 1, 7
- 8 + 1 > 7 (True)
- 8 + 7 > 1 (True)
- 1 + 7 > 8 (True)
Therefore, the side measures 8, 1, 7 can form a triangle.
2. For the group of side measures: 12, 10, 22
- 12 + 10 > 22 (False)
- 12 + 22 > 10 (True)
- 10 + 22 > 12 (True)
Therefore, the side measures 12, 10, 22 cannot form a triangle.
3. For the group of side measures: 2, 7, 6
- 2 + 7 > 6 (True)
- 2 + 6 > 7 (True)
- 7 + 6 > 2 (True)
Therefore, the side measures 2, 7, 6 can form a triangle.
4. For the group of side measures: 9, 4, 3
- 9 + 4 > 3 (True)
- 9 + 3 > 4 (True)
- 4 + 3 > 9 (False)
Therefore, the side measures 9, 4, 3 cannot form a triangle.
Therefore, the groups of side measures that can form a triangle are:
- 8, 1, 7
- 2, 7, 6