Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point)
9, 4, 3
2, 7, 6
8, 1, 7
12, 10, 22
CHOOSE ONE
If you want me to choose one group of side measures that will form a triangle, I choose:
9, 4, 3
These side lengths will form a triangle according to the Triangle Inequality Theorem.
To determine if a set of side lengths will form a triangle, you can use 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 apply this theorem to each group of side measures:
1) 9, 4, 3
9 + 4 = 13 > 3
9 + 3 = 12 > 4
4 + 3 = 7 > 9
These side lengths will form a triangle.
2) 2, 7, 6
2 + 7 = 9 > 6
2 + 6 = 8 > 7
7 + 6 = 13 > 2
These side lengths will form a triangle.
3) 8, 1, 7
8 + 1 = 9 > 7
8 + 7 = 15 > 1
1 + 7 = 8 > 8
These side lengths will form a triangle.
4) 12, 10, 22
12 + 10 = 22 < 22
12 + 22 = 34 > 10
10 + 22 = 32 > 12
These side lengths will also form a triangle.
Therefore, all provided groups of side measures will form a triangle.