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)
According to the Triangle Inequality Theorem, the length of any side of a triangle must be less than the sum of the lengths of the other two sides.
Let's consider the given side lengths: 6 and 2.
For the third side to form a triangle, the sum of the lengths of the other two sides must be greater than the length of the third side.
Case 1: 6 + 2 > x, where x is the third side.
8 > x
Case 2: 6 + x > 2, where x is the third side.
x > -4 (This inequality is not valid since we can't have negative lengths.)
Case 3: 2 + x > 6, where x is the third side.
x > 4
Considering both Case 1 and Case 3, the range of possible values for the third side, x, is:
4 < x < 8
Since we are looking for whole number measures, the possible values for the third side are:
5, 6, and 7 (since they fall within the range 4 < x < 8).
Listing them in ascending order: 5, 6, 7.