To determine which group of side measures will form a triangle, we can use 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 apply this theorem to each group of side measures:
1) 2, 7, 6
The sum of the first two sides is 2 + 7 = 9, which is greater than the third side (6).
The sum of the second and third sides is 7 + 6 = 13, which is greater than the first side (2).
The sum of the first and third sides is 2 + 6 = 8, which is greater than the second side (7).
Therefore, the group of side measures 2, 7, 6 will form a triangle.
2) 9, 4, 3
The sum of the first two sides is 9 + 4 = 13, which is greater than the third side (3).
The sum of the second and third sides is 4 + 3 = 7, which is less than the first side (9).
Therefore, the group of side measures 9, 4, 3 will NOT form a triangle.
3) 8, 1, 7
The sum of the first two sides is 8 + 1 = 9, which is greater than the third side (7).
The sum of the second and third sides is 1 + 7 = 8, which is less than the first side (8).
Therefore, the group of side measures 8, 1, 7 will NOT form a triangle.
4) 12, 10, 22
The sum of the first two sides is 12 + 10 = 22, which is greater than the third side (22).
The sum of the second and third sides is 10 + 22 = 32, which is greater than the first side (12).
The sum of the first and third sides is 12 + 22 = 34, which is greater than the second side (10).
Therefore, the group of side measures 12, 10, 22 will form a triangle.
So, the groups of side measures that will form a triangle are:
- 2, 7, 6
- 12, 10, 22
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