Apply the Triangle Inequality Theorem and determine which option could be the third side of a triangle if the first two sides measure 4 and 6.(1 point) Responses 2 2 11 11 1 1 9
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
If the first two sides measure 4 and 6, then the potential options for the third side would be:
- 2
- 11
- 1
- 9
To determine which option could be the third side of a triangle, we need to check if the sum of the lengths of the first two sides is greater than the length of each potential third side.
Checking each option:
- For 2: 4 + 6 > 2, which is true.
- For 11: 4 + 6 > 11, which is true.
- For 1: 4 + 6 > 1, which is true.
- For 9: 4 + 6 > 9, which is true.
Therefore, all four options: 2, 11, 1, and 9, could be the third side of a triangle.