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.
The measure of the third side could be 5,6,7
In order 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.
For the given triangle with sides measuring 6 and 2, the possible values for the third side can be found by evaluating the following inequalities:
1. 6 + 2 > x
8 > x
2. 6 + x > 2
6 + 2 > x
8 > x
3. 2 + x > 6
8 > x
Therefore, the possible whole number measures of the third side are 5, 6, and 7. Sorting them in ascending order gives: 5, 6, 7.