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
.
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.
Therefore, in this case, the possible whole number measures of the third side would need to satisfy the following inequality:
6 + 2 > x
Simplifying the inequality:
8 > x
Therefore, the possible whole number measures of the third side are 1, 2, 3, 4, 5, 6, and 7 (since they are all less than 8). Now, we just need to list them in ascending order:
1, 2, 3, 4, 5, 6, 7