Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point)
Responses
2, 7, 6
2, 7, 6
9, 4, 3
9, 4, 3
8, 1, 7
8, 1, 7
12, 10, 22
12, 10, 22
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.
Using this theorem, we can determine which group of side measures will form a triangle:
1. 2, 7, 6: The sum of the lengths of the smaller sides (2 + 6 = 8) is greater than the length of the largest side (7). Therefore, these side measures will form a triangle.
2. 9, 4, 3: The sum of the lengths of the smaller sides (3 + 4 = 7) is greater than the length of the largest side (9). Therefore, these side measures will form a triangle.
3. 8, 1, 7: The sum of the lengths of the smaller sides (1 + 7 = 8) is equal to the length of the largest side (8). Therefore, these side measures will form a degenerate triangle, which is a straight line.
4. 12, 10, 22: The sum of the lengths of the smaller sides (10 + 12 = 22) is equal to the length of the largest side (22). Therefore, these side measures will form a degenerate triangle, which is a straight line.