Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.
9, 4, 3
12, 10, 22
2, 7, 6
8, 1, 7
To apply the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
For the group of side measures:
9, 4, 3
Using the theorem, we have:
9 + 4 > 3 (True)
9 + 3 > 4 (True)
4 + 3 > 9 (False)
Since one of the inequalities is false, the group of side measures, 9, 4, 3, will not form a triangle.
For the group of side measures:
12, 10, 22
Using the theorem, we have:
12 + 10 > 22 (False)
12 + 22 > 10 (True)
10 + 22 > 12 (True)
Since two of the inequalities are true, the group of side measures, 12, 10, 22, will not form a triangle.
For the group of side measures:
2, 7, 6
Using the theorem, we have:
2 + 7 > 6 (True)
2 + 6 > 7 (True)
7 + 6 > 2 (True)
Since all three inequalities are true, the group of side measures, 2, 7, 6, will form a triangle.
For the group of side measures:
8, 1, 7
Using the theorem, we have:
8 + 1 > 7 (True)
8 + 7 > 1 (True)
1 + 7 > 8 (True)
Since all three inequalities are true, the group of side measures, 8, 1, 7, will form a triangle.