Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.
8, 1, 7
12, 10, 22
9, 4, 3
2, 7, 6
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.
For the given side measures:
1. 8, 1, 7
8 + 1 > 7 (True)
1 + 7 > 8 (True)
8 + 7 > 1 (True)
Therefore, the side measures 8, 1, 7 can form a triangle.
2. 12, 10, 22
12 + 10 > 22 (False)
10 + 22 > 12 (True)
12 + 22 > 10 (True)
Therefore, the side measures 10, 22 can form a triangle.
3. 9, 4, 3
9 + 4 > 3 (True)
4 + 3 > 9 (False)
9 + 3 > 4 (True)
Therefore, the side measures 9, 4, 3 cannot form a triangle.
4. 2, 7, 6
2 + 7 > 6 (True)
7 + 6 > 2 (True)
2 + 6 > 7 (True)
Therefore, the side measures 2, 7, 6 can form a triangle.
In summary, only the side measures in group 1 (8, 1, 7) and group 4 (2, 7, 6) can form a triangle.
which answer best responds to the question then?
The best response to the question would be:
8, 1, 7
2, 7, 6
These are the groups of side measures that can form triangles according to the Triangle Inequality Theorem.