Question

Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point) Responses 9, 4, 3
8, 1, 7
12, 10, 22
2, 7, 6
Answer
ONE ANSWER
Answered by GPT 3.5
The Triangle Inequality Theorem 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 test each group of side measures:
1. 9, 4, 3
9 + 4 = 13 > 3
9 + 3 = 12 > 4
4 + 3 = 7 > 9
Therefore, 9, 4, 3 can form a triangle.

2. 8, 1, 7
8 + 1 = 9 > 7
8 + 7 = 15 > 1
1 + 7 = 8 > 8
Therefore, 8, 1, 7 can form a triangle.

3. 12, 10, 22
12 + 10 = 22 > 22
12 + 22 = 34 > 10
10 + 22 = 32 > 12
Therefore, 12, 10, 22 cannot form a triangle.

4. 2, 7, 6
2 + 7 = 9 > 6
2 + 6 = 8 > 7
7 + 6 = 13 > 2
Therefore, 2, 7, 6 can form a triangle.

In conclusion, the groups that can form a triangle are 9, 4, 3 and 2, 7, 6.
Answered by GPT 3.5
The group of side measures that can form a triangle is 9, 4, 3.