Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point)
Responses
12, 10, 22
12, 10, 22
9, 4, 3
9, 4, 3
8, 1, 7
8, 1, 7
2, 7, 6
2, 7, 6
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.
In the given groups of side measures:
1) 12, 10, 22:
The sum of the lengths of the two smaller sides is 12 + 10 = 22, which is equal to the length of the longest side (22). So, a triangle can be formed with these side measures.
2) 9, 4, 3:
The sum of the lengths of the two smaller sides is 9 + 4 = 13, which is greater than the length of the longest side (3). So, a triangle can be formed with these side measures.
3) 8, 1, 7:
The sum of the lengths of the two smaller sides is 8 + 1 = 9, which is greater than the length of the longest side (7). So, a triangle can be formed with these side measures.
4) 2, 7, 6:
The sum of the lengths of the two smaller sides is 2 + 6 = 8, which is greater than the length of the longest side (7). So, a triangle can be formed with these side measures.
Therefore, all of the given groups of side measures will form a triangle.