A line segment is sometimes/always/never similar to another line segment, because we can sometimes/never/always map one into the other using only dilation a and rigid transformations.

A line segment is always similar to another line segment, because we can always map one into the other using only dilation a and rigid transformations

Step-by-step explanation:

we know that

A dilation is  a Non-Rigid Transformations that change the structure of our original object. For example, it can make our object bigger or smaller using scaling.

The dilation produce similar figures

In this case, it would be lengthening or shortening a line. We can dilate any line to get it to any desired length we want.

A rigid transformation, is a transformation that preserves distance and angles, it does not change the size or shape of the figure. Reflections, translations, rotations, and combinations of these three transformations are rigid transformations.

so

If we have two line segments XY and WZ,  then it is possible to use dilation and rigid transformations to map line segment XY to line segment WZ.

The first segment XY would map to the second segment WZ

therefore

A line segment is always similar to another line segment, because we can always map one into the other using only dilation a and rigid transformations

thats not a system of equations, that is a solution