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 2 and 6. List them in ascending order.
A. 5; 6; 7
B. 8; 9; 10
C. 11; 12; 13
D. 0; 0; 1
To apply the Triangle Inequality Theorem, we need to find the possible range of values for the third side of a triangle when given the lengths of the first two sides.
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.
In this case, the lengths of the first two sides are 2 and 6.
Possible values for the third side can be found by considering the sum of the lengths of the first two sides:
- For the sum of the lengths to be greater than 2 but less than 6, the third side must be larger than 2 but smaller than 6, so the possible range is (2, 6).
- For the sum of the lengths to be greater than 6, the third side must be larger than 6, so the possible range is (6, ∞) or simply [7, ∞). Note that the third side cannot be equal to 6, as it would result in a degenerate triangle.
Therefore, the possible whole number measures of the third side of a triangle with the first two sides measuring 2 and 6 are the numbers in the range (2, 6), excluding 6. These numbers are 3, 4, and 5.
Listing them in ascending order, the possible whole number measures of the third side are: 3, 4, 5.
The correct answer is: A. 5; 6; 7