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 __, __, or __,
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.
In this case, if the first two sides measure 6 and 2, we can calculate the possible range for the third side:
6 + 2 > x
8 > x
So the third side must be less than 8. It also must be greater than the difference of the two sides:
6 - 2 < x
4 < x
So the third side must be greater than 4.
Combining both conditions, the possible whole number measures of the third side are: 5, 6, or 7.
Therefore, the measure of the third side could be 5, 6, or 7.