Apply the triangle equality theorem to determine the possible whole number measures of the third side of a triangle if the first two sides measure six and two lists them in ascending order
The triangle inequality theorem states that for a triangle with side lengths a, b, and c, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, the first two sides measure six and two. Let's label them as a = 6 and b = 2.
To find the range of possible whole number measures for the third side, we need to use the triangle inequality theorem. We have two cases to consider:
1) The third side is shorter than the difference of the first two sides.
In this case, c < a - b. Substituting the given values, c < 6 - 2, c < 4.
2) The third side is longer than the difference of the first two sides but shorter than their sum.
In this case, a - b < c < a + b. Substituting the given values, 6 - 2 < c < 6 + 2, 4 < c < 8.
Combining both cases, we can conclude that the possible whole number measures of the third side lie between 4 and 8, excluding both 4 and 8. Therefore, the ascending order list of possible measures is: 5, 6, and 7.