Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point) Responses 8, 1, 7 8, 1, 7 12, 10, 22 12, 10, 22 9, 4, 3 9, 4, 3 2, 7, 6
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 set of side measures:
1) 8, 1, 7
8 + 1 > 7 (True)
8 + 7 > 1 (True)
1 + 7 > 8 (True)
Since all three inequalities are true, the side measures 8, 1, and 7 will form a triangle.
2) 12, 10, 22
12 + 10 > 22 (False)
12 + 22 > 10 (True)
10 + 22 > 12 (True)
Since one of the inequalities is false, the side measures 12, 10, and 22 will not form a triangle.
3) 9, 4, 3
9 + 4 > 3 (True)
9 + 3 > 4 (True)
4 + 3 > 9 (False)
Since one of the inequalities is false, the side measures 9, 4, and 3 will not form a triangle.
4) 2, 7, 6
2 + 7 > 6 (True)
2 + 6 > 7 (True)
7 + 6 > 2 (True)
Since all three inequalities are true, the side measures 2, 7, and 6 will form a triangle.
Therefore, the groups of side measures that will form a triangle are 8, 1, 7 and 2, 7, 6.