Intersecting and Non-Intersecting Lines
If you draw two lines in a plane, there are only two possibilities: either the two lines will intersect at some point, or they will be parallel – in which case they will never intersect. These two possibilities are shown below:
In the case of two parallel lines, the perpendicular line drawn at any point to one line will be perpendicular to the other line as well (can you see why?). Also, the length of the common perpendicular between the two parallels at any location will always be the same:
In other words, the perpendicular distance between the two lines will stay the same.
There is another interesting fact you should think about. We have seen that any two lines in a plane will either intersect or will be parallel. However, in three-dimensional space, you can have pairs of lines which are neither parallel nor intersect! Can you visualize this?