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.(2 points) The measure of the third side could be ? , ? , or ?.
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.
In this case, the first two sides measure 6 and 2.
Let's analyze the possible combinations:
1) The sum of 6 and 2 must be greater than the third side:
6 + 2 > third side
8 > third side
2) The sum of 2 and the third side must be greater than 6:
2 + third side > 6
third side > 4
Therefore, the possible whole number measures for the third side of the triangle are any values greater than 4 and lesser than 8.
Listing them in ascending order, the possible measures of the third side are: 5, 6, and 7.