apply the triangle inequality theorem to determine the possible whole number measures of the third side of a triangle if the two sides measures 6 and 2. List them in ascending order.

To apply the triangle inequality theorem, we need to compare the sum of the lengths of the two known sides with the length of the unknown side.

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.

Given that the lengths of the two known sides are 6 and 2, we can consider three cases:

1. The sum of the lengths of the two known sides is equal to the length of the third side:
6 + 2 = 8
Since the sum of the lengths is equal to the length of the third side, there are no whole number measures for the third side in this case.

2. The sum of the lengths of the two known sides is less than the length of the third side:
6 + 2 < 3rd side length
8 < 3rd side length
In this case, the third side would not form a triangle.

3. The sum of the lengths of the two known sides is greater than the length of the third side:
6 + 2 > 3rd side length
8 > 3rd side length
In this case, we can consider the possible whole number measures of the third side:

- The third side could be 7.
- The third side could be any whole number greater than 7.

Therefore, the possible whole number measures of the third side, listed in ascending order, would be 7, 8, 9, 10, 11, ...

So, the measures of the third side could be 7, 8, or any whole number greater than 7.