Editing Parallel (geometry) (section)

===Two planes===
Similar to the fact that parallel lines must be located in the same plane, parallel planes must be situated in the same three-dimensional space and contain no point in common.

Two distinct planes ''q'' and ''r'' are parallel if and only if the distance from a point ''P'' in plane ''q'' to the nearest point in plane ''r'' is independent of the location of ''P'' in plane ''q''. This will never hold if the two planes are not in the same three-dimensional space.