parallel lines and a plane

Question

Explain why two parallel lines define a plane.

If I hold two pencils so that they’re parallel, there’s only one position in which a plane can rest on both pencils.But can someone give me a more valid reason? Should I use definition of a plane?

Answer 1

I would like to expand on the comments a little.

Three points indeed define a plane, but if you have two lines, $L1$ and $L2$ you have lots of choices for those three points. Pick any two points on $L1$ to start, and then we need to pick one point on $L2$ to define our plane. If the lines are not parallel, then your choice matters a lot! But if the lines are parallel, then it doesn't matter which point you pick on $L2$ -- every choice gives the same plane.