Final answer:
After rotating parallel lines around a point on one of the lines, the lines remain parallel because rotation maintains equal distances between points.
Step-by-step explanation:
When rotating parallel lines around a point that lies on one of the lines, the result is that the lines will remain parallel. This is because a rotation is a type of transformation that turns every point of a figure through a specified angle and direction around a fixed point, called the center of rotation. As the lines start parallel and equal distances from one another, after rotation they will still be the same distance apart at every point and therefore stay parallel.