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.
The measure of the third side could be, , or .
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.
So, in this case, the third side must be greater than the difference between the first two sides and less than the sum of the first two sides.
The difference between 6 and 2 is 4, so the third side must be greater than 4.
The sum of 6 and 2 is 8, so the third side must be less than 8.
Therefore, the possible whole number measures of the third side are 5, 6, and 7.
Listing them in ascending order, the possible measures of the third side are: 5, 6, 7.
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To apply the Triangle Inequality Theorem, we need to find the possible range of values for the third side of the triangle. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given that the first two sides measure 6 and 2, let's find the possible range for the third side.
1. The sum of the first two sides: 6 + 2 = 8
2. The possible range for the third side can be greater than 8.
To list the possible whole number measures of the third side in ascending order, we can start with the smallest whole number greater than 8.
So, the possible whole number measures of the third side, in ascending order, are: 9, 10, 11, ...
To apply the Triangle Inequality Theorem, we need to remember that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given that the first two sides measure 6 and 2, we need to find the range of possible values for the third side.
First, let's consider the minimum possible value for the third side. The sum of the first two sides should be greater than the third side. In this case, 6 + 2 = 8. So, the minimum possible value for the third side is 8.
Next, let's consider the maximum possible value for the third side. The third side should also be less than the sum of the first two sides. In this case, the maximum value for the third side is 6 + 2 - 1 = 7.
Therefore, the possible whole number measures of the third side, in ascending order, are 8 and 7.