What does it mean for one line to be parallel to another?

Question

What does it mean for one line to be parallel to another?

Answer 1

For two lines to be parallel to each other then all of the following MUST be true:

 

1) The slope of a line is written as y = mx + b.  For both lines to be parallel then the value for m must be the same.

2) Both lines must be contained in one (and only one) unique plane that contains both of them.

3) Any line that intersects both of them must create alternate interior angles, alternate exterior angles, and corresponding angles that are congruent.

4) Finally, and most obviously the two lines must never have the ability to meet.  However, 4) does not make them parallel (they could be skewed lines) unless 1) is also true.

 

Hope this helps.