Question
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
8, 1, 7
8, 1, 7
2, 7, 6
2, 7, 6
12, 10, 22
12, 10, 22
According to the Triangle Inequality Theorem, for a group of side measures to form a triangle, 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:
- 9, 4, 3: The sum of the lengths of the two shorter sides (4 + 3 = 7) is greater than the length of the longest side (9). Therefore, this group can form a triangle.
- 8, 1, 7: The sum of the lengths of the two shorter sides (1 + 7 = 8) is equal to the length of the longest side (8). Therefore, this group cannot form a triangle.
- 2, 7, 6: The sum of the lengths of the two shorter sides (2 + 6 = 8) is greater than the length of the longest side (7). Therefore, this group can form a triangle.
- 12, 10, 22: The sum of the lengths of the two shorter sides (10 + 12 = 22) is equal to the length of the longest side (22). Therefore, this group cannot form a triangle.