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 (least to greatest).(9 points)
To apply 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.
Let's call the third side of the triangle x.
By applying the Triangle Inequality Theorem, we have the following inequalities:
6 + 2 > x and 6 + x > 2 and 2 + x > 6
Simplifying these inequalities, we find:
8 > x and 6 > x and x > 4
So the possible measures of the third side (x) are between 4 and 6 (exclusive), inclusive is 5.
Therefore, the possible whole number measures of the third side of the triangle, in ascending order, are: 5.