Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.
A) 12, 10, 22
B) 8, 1, 7
C) 9, 4, 3
D) 2, 7, 6
According to the Triangle Inequality Theorem, in order 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.
Let's apply the theorem to each of the given options:
A) 12, 10, 22
12 + 10 = 22 > 22 (The sum of the two smaller sides is greater than the longest side.) The triangle inequality theorem holds true for this option.
B) 8, 1, 7
1 + 7 = 8 > 8 (The sum of the two smaller sides is greater than the longest side.) The triangle inequality theorem holds true for this option too.
C) 9, 4, 3
4 + 3 = 7 < 9 (The sum of the two smaller sides is not greater than the longest side.) The triangle inequality theorem is not satisfied for this option.
D) 2, 7, 6
2 + 6 = 8 < 7 (The sum of the two smaller sides is not greater than the longest side.) Once again, the triangle inequality theorem is not satisfied for this option.
Therefore, the groups of side measures that will form a triangle are A) 12, 10, 22, and B) 8, 1, 7.