10. 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
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.
In this case, the first two sides measure 2 and 6. So, we can check the possible values for the third side by adding or subtracting the known lengths:
For the third side to be greater than 2 but less than 8, it can have the possible values: 3, 4, 5, 6, or 7.
Among these values, only 5; 6; 7 are whole numbers.
Therefore, the possible whole number measures of the third side of the triangle are 5, 6, and 7.
The correct answer is A. 5; 6; 7.