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
.
By the Triangle Inequality Theorem, the measure of the third side of a triangle must be less than the sum of the measures of the other two sides and greater than the difference between the measures of the other two sides.
The first two sides measure 6 and 2. Therefore, the possible measures for the third side are:
- Less than 6 + 2 = 8
- Greater than 6 - 2 = 4
Possible whole number measures for the third side in ascending order are: 5, 6, and 7.