Apply the Triangle Inequality Theorem to determine the possible whole number measure of the third side of a triangle if the first two sides measure 6 and 2. List then in ascending order. (2 points)
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.
Let's denote the first side as 6 and the second side as 2.
Case 1:
We can consider the first side (6) and the second side (2) as the two sides, and calculate the possible range for the third side.
6 + 2 > x
8 > x
In this case, the possible whole number measures for the third side (x) are 1, 2, 3, 4, 5, 6, and 7.
Case 2:
We can consider the first side (6) and the third side as the two sides, and calculate the possible range for the second side.
6 + x > 2
x > -4
Since the lengths of the sides cannot be negative, we exclude negative values.
Case 3:
We can consider the second side (2) and the third side as the two sides, and calculate the possible range for the first side.
2 + x > 6
x > 4
Since the lengths of the sides cannot be negative, we exclude negative values.
Combining all the cases, the possible whole number measures of the third side, in ascending order, are 1, 2, 3, 4, 5, 6, and 7.