Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point)
Responses
2, 7, 6
2, 7, 6
9, 4, 3
9, 4, 3
12, 10, 22
12, 10, 22
8, 1, 7
To determine which group of side measures will form a triangle, we can 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 calculate the sum of the two smaller sides and compare it to the length of the largest side in each group:
1. For the group 2, 7, 6:
2 + 6 = 8 > 7 (True)
2 + 7 = 9 > 6 (True)
6 + 7 = 13 > 2 (True)
Therefore, the measures 2, 7, and 6 can form a triangle.
2. For the group 9, 4, 3:
9 + 3 = 12 > 4 (True)
9 + 4 = 13 > 3 (True)
3 + 4 = 7 > 9 (False)
Therefore, the measures 9, 4, and 3 cannot form a triangle.
3. For the group 12, 10, 22:
12 + 10 = 22 > 22 (False)
12 + 22 = 34 > 10 (True)
10 + 22 = 32 > 12 (True)
Therefore, the measures 12, 10, and 22 can form a triangle.
4. For the group 8, 1, 7:
8 + 1 = 9 > 7 (True)
8 + 7 = 15 > 1 (True)
1 + 7 = 8 > 8 (False)
Therefore, the measures 8, 1, and 7 cannot form a triangle.
Therefore, the group of side measures that can form a triangle is 2, 7, 6 and 12, 10, 22.