.

Also, do parallel lines eventually meet?

Actually parallel lines cannot meet at apoint or intersect because they are defined that way, if twolines will intersect then they will not remain parallellines.

Also, do parallel lines intersect on a sphere? Parallel lines do not exist in sphericalgeometry. Any straight line through a point P on asphere is by definition a great circle. Two great circleswill intersect at two points at a Euclidean segment, whichis the diameter of the sphere. There are no parallellines in spherical geometry.

Consequently, how many times can two parallel lines meet?

Two parallel lines will cross exactly once at theline at infinity -- again we see two images of thatcrossing when we turn around, but they are by definition the samepoint. And any line in the plane will cross theline at infinity once.

Do parallel lines never intersect?

In geometry, parallel lines are lines in aplane which do not meet; that is, two lines in aplane that do not intersect or touch each other at any pointare said to be parallel. By extension, a line and aplane, or two planes, in three-dimensional Euclidean space thatdo not share a point are said to beparallel.