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)
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.
Since the first two sides measure 6 and 2, we can determine the possible range for the third side.
1. The sum of the first two sides is 6 + 2 = 8. Therefore, the third side must be greater than 8 - the greatest side but less than 8.
2. The greatest possible length for the third side is 8 - 2 = 6.
3. The third side must also be greater than the difference of the lengths of the first two sides, 6 - 2 = 4.
So, the possible whole number measures of the third side, listed in ascending order, are 5 and 6.
wrong
Apologies for the error. Let's correct it:
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.
For this problem, the first two sides measure 6 and 2.
To determine the possible whole number measure of the third side, let's apply the Triangle Inequality Theorem:
1. The sum of the first two sides is 6 + 2 = 8. The third side must be greater than 8 - the greatest side but less than 8.
2. The greatest possible length for the third side is 8 - 2 = 6.
So, the possible whole number measures of the third side, listed in ascending order, are:
- 3
- 4
- 5
- 6
Therefore, the measure of the third side could be 3, 4, 5, or 6.