Question
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 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.
Given that the first two sides measure 6 and 2, we can determine the range of possible measures for the third side:
1. 6 + 2 > third side
2. 6 + third side > 2
3. 2 + third side > 6
Solving these inequalities:
1. 8 > third side
2. 6 > third side
3. 2 > third side
Therefore, the possible measures for the third side are any whole number between 3 and 7 inclusive. Listing them in ascending order: 3, 4, 5, 6, 7.