
 Two points must have a line in common
 Two planes must have a line in common
 Two lines can, but need not, have a plane in common
 If two lines have a plane in common, they must have exactly one point in common—never more, and never none
 If two lines do not have a plane in common, they are skew, and have nothing at all in common
 Three points have exactly one plane in common—never more, and never none
 Three planes have exactly one point in common—never more, and never none
Note the general (and remarkable) interchangeability here
of point and plane, or of point and line.
Compare, for example, axioms (6) and (7).
This is called Duality.
We emphasise that, by (4) in this list, lines with a common plane must meet , and that, by (5),
lines that do not meet cannot be other than skew.
Animation illustrating that Only Skew Lines Do Not Meet
We emphasise, too, that taking an element common to other elements to be part of (in the sense of “incorporated into”) these other elements is a fundamental error. For example,
 the point common to two lines is simply the place where the lines meet; the meetingplace is part of neither line,
because lines are not points.
 the line common to two planes is simply the line in which the planes meet; the meetingline is part of neither plane,
because planes are not lines.

