Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.
A. 8, 1, 7
B. 2, 7, 6
C. 12, 10, 22
D. 9, 4, 3
To determine if a 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.
For option A:
8 + 1 = 9 > 7.
1 + 7 = 8 > 8.
8 + 7 = 15 > 1.
Therefore, the side measures 8, 1, and 7 will form a triangle.
For option B:
2 + 7 = 9 > 6.
2 + 6 = 8 > 7.
7 + 6 = 13 > 2.
Therefore, the side measures 2, 7, and 6 will form a triangle.
For option C:
12 + 10 = 22 > 22.
12 + 22 = 34 > 10.
10 + 22 = 32 > 12.
Therefore, the side measures 12, 10, and 22 will form a triangle.
For option D:
9 + 4 = 13 > 3.
9 + 3 = 12 > 4.
4 + 3 = 7 < 9.
Therefore, the side measures 9, 4, and 3 will not form a triangle.
Therefore, the groups of side measures that will form a triangle are:
A. 8, 1, 7
B. 2, 7, 6
C. 12, 10, 22