Question

Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point)
Responses

8, 1, 7
8, 1, 7

9, 4, 3
9, 4, 3

12, 10, 22
12, 10, 22

2, 7, 6

Answer 1

choose one answer

Answer 2

According to the Triangle Inequality Theorem, for a triangle to be formed, the sum of the lengths of any two sides must be greater than the length of the third side.

Applying this theorem to the given side measures:

1) 8, 1, 7
8 + 1 = 9 (which is greater than 7)
1 + 7 = 8 (which is greater than 8)
7 + 8 = 15 (which is greater than 1)
Since the sum of the lengths of any two sides is greater than the length of the third side for all combinations, this group of side measures will form a triangle.

2) 9, 4, 3
9 + 4 = 13 (which is greater than 3)
4 + 3 = 7 (which is greater than 9)
3 + 9 = 12 (which is greater than 4)
Since the sum of the lengths of any two sides is greater than the length of the third side for all combinations, this group of side measures will form a triangle.

3) 12, 10, 22
12 + 10 = 22 (which is equal to 22, but not greater)
10 + 22 = 32 (which is greater than 12)
22 + 12 = 34 (which is greater than 10)
Since the sum of the lengths of any two sides is not greater than the length of the third side for one combination, this group of side measures will not form a triangle.

4) 2, 7, 6
2 + 7 = 9 (which is greater than 6)
7 + 6 = 13 (which is greater than 2)
6 + 2 = 8 (which is greater than 7)
Since the sum of the lengths of any two sides is greater than the length of the third side for all combinations, this group of side measures will form a triangle.

Therefore, the groups of side measures that will form a triangle are:
- 8, 1, 7
- 9, 4, 3
- 2, 7, 6

Answer 3

The group of side measures that will form a triangle is:

9, 4, 3