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 1 1 9 9 11
To apply the Triangle Inequality Theorem, we need to check if the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Let's check each option:
- 2: 4 + 2 = 6 which is equal to 6, so this is NOT a valid option.
- 1: 4 + 1 = 5 which is less than 6, so this is NOT a valid option.
- 9: 4 + 9 = 13 which is greater than 6, so this IS a valid option.
- 11: 4 + 11 = 15 which is greater than 6, so this IS a valid option.
Therefore, the valid options for the third side of a triangle with sides measuring 4 and 6 are 9 and 11.