Apply the Triangle Inequality Theorem to determine the possible whole number measures of the third side of a triangle if the first two sides measure 6 and 2. List them in ascending order.(2 points) The measure of the third side could be __, __, or __.

Answer 1

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given sides of length 6 and 2, the possible measures for the third side can be found by checking whether the sum of the known sides is greater than the unknown third side:

1. Third side = 6 + 2 = 8 (8 is valid, since 8 > 6)
2. Third side = 6 - 2 = 4 (4 is valid, since 4 > 2)
3. Third side = 6 + 2 = 4 (4 is not valid, since 4 is not greater than 6)

Therefore, the possible whole number measures of the third side, in ascending order, are 4, 4, and 8.