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

1 answer

Based on the Triangle Inequality Theorem, a triangle can be formed if the sum of the lengths of any two sides is greater than the length of the third side.

1. For the sides 9, 4, 3: 9 + 4 = 13 > 3, 9 + 3 = 12 > 4, 4 + 3 = 7 > 9.
Therefore, the sides 9, 4, 3 can form a triangle.

2. For the sides 12, 10, 22: 12 + 10 = 22 > 22, 12 + 22 = 34 > 10, 10 + 22 = 32 > 12.
Therefore, the sides 12, 10, 22 cannot form a triangle.

3. For the sides 2, 7, 6: 2 + 7 = 9 > 6, 2 + 6 = 8 > 7, 7 + 6 = 13 > 2.
Therefore, the sides 2, 7, 6 can form a triangle.

4. For the sides 8, 1, 7: 8 + 1 = 9 > 7, 8 + 7 = 15 > 1, 1 + 7 = 8 < 8.
Therefore, the sides 8, 1, 7 cannot form a triangle.

Therefore, the group of side measures that can form a triangle are 9, 4, 3 and 2, 7, 6.