Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point)
2, 7, 6
9, 4, 3
12, 10, 22
8, 1, 7
To determine if a 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 remaining side.
1) For the side measures 2, 7, 6:
2 + 6 = 8, which is greater than 7.
7 + 6 = 13, which is greater than 2.
2 + 7 = 9, which is greater than 6.
Therefore, the side measures 2, 7, 6 will form a triangle.
2) For the side measures 9, 4, 3:
9 + 3 = 12, which is greater than 4.
3 + 4 = 7, which is not greater than 9.
9 + 4 = 13, which is greater than 3.
Therefore, the side measures 9, 4, 3 will form a triangle.
3) For the side measures 12, 10, 22:
12 + 10 = 22, which is equal to 22.
10 + 22 = 32, which is greater than 12.
12 + 22 = 34, which is greater than 10.
Therefore, the side measures 12, 10, 22 will form a triangle.
4) For the side measures 8, 1, 7:
8 + 1 = 9, which is greater than 7.
1 + 7 = 8, which is not greater than 8.
8 + 7 = 15, which is greater than 1.
Therefore, the side measures 8, 1, 7 will form a triangle.