Points and lines in a plane

The following points describe some necessary ideas.

• A point either lies on a line or does not lie on a line.
• There is exactly one line passing through two distinct points.
• Two distinct lines in the plane either meet at a point or are parallel.
• Two lines in a plane are called parallel if they never meet, no matter how far they are produced (meaning extended). This is written AB || PG.
• Two lines parallel to a third line are parallel to each other.
• Three points that all lie on the one line are called collinear.
• Three lines that all pass through one point are called concurrent.