Which of the following statements about parallel lines is false?

The statement that parallel lines can cross is false because, by definition, parallel lines are lines in a plane that are always the same distance apart and never meet or intersect, regardless of how far they are extended in either direction. This characteristic distinguishes parallel lines from other types of lines, as they maintain a consistent distance from one another.

In contrast, the other statements regarding parallel lines are true. They can run horizontally, as many parallel lines do in a typical Cartesian coordinate system or similar frameworks. Similarly, parallel lines can run vertically, which is often observed when dealing with lines oriented along the y-axis. Thus, these orientations do not affect their parallel nature; they will still remain equidistant and never intersect.