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
2, 7, 6
2, 7, 6
8, 1, 7
8, 1, 7
12, 10, 22
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 apply this theorem to each group of side measures:
1. 9, 4, 3
9 + 4 > 3 (true)
9 + 3 > 4 (true)
4 + 3 > 9 (false)
Since one of the sums is not greater than the third side, this group of side measures cannot form a triangle.
2. 2, 7, 6
2 + 7 > 6 (true)
2 + 6 > 7 (true)
7 + 6 > 2 (true)
All sums are greater than the third side, so this group of side measures can form a triangle.
3. 8, 1, 7
8 + 1 > 7 (true)
8 + 7 > 1 (true)
1 + 7 > 8 (true)
All sums are greater than the third side, so this group of side measures can form a triangle.
4. 12, 10, 22
12 + 10 > 22 (false)
12 + 22 > 10 (true)
10 + 22 > 12 (true)
Only one of the sums is greater than the third side, so this group of side measures cannot form a triangle.
Therefore, the groups of side measures that would form a triangle are 2, 7, 6 and 8, 1, 7.