Parallelism of a line and a plane, and of two planes

Two planes either intersect (along a common line) or are parallel (no common point). Criterion: if two intersecting lines of one plane are parallel to two lines of another plane, respectively, the planes are parallel. Properties: if a third plane cuts two parallel planes, the lines of intersection are parallel; through a point outside a plane exactly one plane parallel to it can be drawn; two planes parallel to a third plane are parallel to each other. Segments of parallel lines between parallel planes are equal, since they are opposite sides of a parallelogram. Three parallel planes cut proportional segments from two lines: AB : BC = A₁B₁ : B₁C₁ (the spatial form of Thales’ theorem). Opposite faces of a parallelepiped lie in parallel planes, so its lateral edges are equal.