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.
Given that the first two sides measure 6 and 2, we can determine the range of possible measures for the third side using the Triangle Inequality Theorem:
6 + 2 > x
8 > x
2 + x > 6
x > 4
6 + x > 2
x > -4
Since the third side must be a whole number, the possible measures are 5, 6, and 7. These values are listed in ascending order:
5, 6, 7