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.
According to the Triangle Inequality Theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Given that the first two sides measure 2 and 6, let's consider the possible measures of the third side, x:
1. 2 + 6 > x ⇒ 8 > x
2. 2 + x > 6 ⇒ x > 4
3. 6 + x > 2 ⇒ x > -4
Combining the inequalities, we get:
4 < x < 8
Therefore, the possible whole number measures of the third side of the triangle are 5, 6, and 7 (in ascending order).