Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point) Responses 9, 4, 3 9, 4, 3 12, 10, 22 12, 10, 22 2, 7, 6 2, 7, 6 8, 1, 7
The Triangle Inequality Theorem 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 the Triangle Inequality Theorem to the given side measures:
1. For side measures 9, 4, 3:
9 + 4 = 13 > 3 (true)
9 + 3 = 12 > 4 (true)
4 + 3 = 7 > 9 (false)
Since 4 + 3 is not greater than 9, this group of side measures will NOT form a triangle.
2. For side measures 12, 10, 22:
12 + 10 = 22 > 22 (false)
12 + 22 = 34 > 10 (true)
10 + 22 = 32 > 12 (true)
Since 12 + 10 is not greater than 22, this group of side measures will NOT form a triangle.
3. For side measures 2, 7, 6:
2 + 7 = 9 > 6 (true)
2 + 6 = 8 > 7 (true)
7 + 6 = 13 > 2 (true)
Since all combinations of two sides satisfy the Triangle Inequality Theorem, this group of side measures WILL form a triangle.
4. For side measures 8, 1, 7:
8 + 1 = 9 > 7 (true)
8 + 7 = 15 > 1 (true)
1 + 7 = 8 > 8 (false)
Since 1 + 7 is not greater than 8, this group of side measures will NOT form a triangle.
Therefore, the group of side measures that will form a triangle is 2, 7, 6.