The possible values of the the length of one side of a triangle lie in a range between the sum and the difference of the other two.
In this case, that would be 0 < xy < 12
In this case, that would be 0 < xy < 12
In this case, we are given that XZ is 6 units long and YZ is also 6 units long. We want to find the possible measures for XY.
To apply the triangle inequality theorem, we need to consider all the possible combinations of side lengths. Let's explore the different cases:
1) XZ + YZ > XY:
Substituting the given values, we have 6 + 6 > XY.
Simplifying the expression, we get 12 > XY.
2) XZ + XY > YZ:
Substituting the given values, we have 6 + XY > 6.
Simplifying the expression, we get XY > 0 (since we cannot have a negative length).
3) YZ + XY > XZ:
Substituting the given values, we have 6 + XY > 6.
Simplifying the expression, we get XY > 0 (since we cannot have a negative length).
From the above cases, we can conclude that XY must be greater than 0 and less than 12 (i.e., 0 < XY < 12). This means that any value of XY within this range would satisfy the triangle inequality theorem.
Thus, the possible measures for line segment XY in triangle XYZ are any real numbers between 0 and 12.