Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.
A. 12, 10, 22
B. 2, 7, 6
C. 9, 4, 3
D. 8, 1, 7
To determine if a set of three side lengths can form a triangle, we must 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 group of side measures:
A. 12, 10, 22
12 + 10 = 22 which is greater than 22. But 12 + 22 = 34 which is not greater than 10. Therefore, a triangle cannot be formed with these side measures.
B. 2, 7, 6
2 + 7 = 9 which is greater than 6
2 + 6 = 8 which is not greater than 7
7 + 6 = 13 which is greater than 2
Therefore, a triangle can be formed with these side measures.
C. 9, 4, 3
These side measures cannot form a triangle as 4 + 3 is not greater than 9.
D. 8, 1, 7
1 + 7 = 8 which is equal to 8. But 1 + 8 = 9 which is greater than 7. And 7 + 8 = 15 which is greater than 1. Therefore, a triangle can be formed with these side measures.
So, the group of side measures that will form a triangle is B. 2, 7, 6.