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
According to the Triangle Inequality Theorem, for a triangle to be formed, the sum of the lengths of any two sides must be greater than the length of the third side.
A. 8 + 1 = 9 > 7, 1 + 7 = 8 > 8, 8 + 7 = 15 > 1
B. 2 + 7 = 9 > 6, 2 + 6 = 8 > 7, 7 + 6 = 13 > 2
C. 12 + 10 = 22 = 22, 12 + 22 = 34 > 10, 10 + 22 = 32 > 12
D. 9 + 4 = 13 > 3, 9 + 3 = 12 > 4, 4 + 3 = 7 > 9
Based on the Triangle Inequality Theorem, the group of side measures that will form a triangle is option B: 2, 7, 6.