At lunch today we were talking about maps and lines of longitude etc (9th grade earth science) and I commented on the interesting fact that two people could start at different points on the equator and head north, their directions being parallel to one another, and end up meeting at the north pole. I gave this as an example of two parallel lines intersecting. (Wanting to appear clever :) )
Then a colleague said, "so how do you know the lines are parallel?"
This is, IMO, a very good question. I did a brief search on "definition parallel lines" on google but found nothing helpful.