Question

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

12, 10, 22
12, 10, 22

9, 4, 3
9, 4, 3

8, 1, 7

Answer 1

To apply the Triangle Inequality Theorem, we need to compare the sum of the lengths of any two sides with the length of the remaining side. If the sum of the lengths of two sides is greater than the length of the third side, then the sides can form a triangle. Otherwise, they cannot.

1) For the group of side measures 2, 7, 6:
2 + 7 > 6 (True)
2 + 6 > 7 (True)
7 + 6 > 2 (True)

Therefore, the group of side measures 2, 7, 6 will form a triangle.

2) For the group of side measures 12, 10, 22:
12 + 10 > 22 (False)

Therefore, the group of side measures 12, 10, 22 will not form a triangle.

3) For the group of side measures 9, 4, 3:
9 + 4 > 3 (True)
9 + 3 > 4 (True)
4 + 3 > 9 (False)

Therefore, the group of side measures 9, 4, 3 will not form a triangle.

4) For the group of side measures 8, 1, 7:
8 + 1 > 7 (True)
8 + 7 > 1 (True)
1 + 7 > 8 (True)

Therefore, the group of side measures 8, 1, 7 will form a triangle.