Use the triangle inequality theorem to determine the possiable whole number measures of the third side of a triangle of the first 2 sides measure 6 and 2. List them in a ascending order
The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, the first two sides measure 6 and 2, respectively. Now we can apply the triangle inequality theorem to find the possible whole number measures of the third side.
1. First, consider the sum of the first two sides:
6 + 2 = 8
2. Now we compare the sum (8) with each individual side length. The sum must be greater than each side length for a valid triangle.
- For the third side to be valid, it must be greater than (8 - 6 = 2).
- For the third side to be valid, it must also be greater than (8 - 2 = 6).
3. Thus, the possible whole number measures for the third side are all integers greater than 2 and less than 6.
Listing them in ascending order, the possible whole number measures for the third side are: 3, 4, and 5.