Perpendicular, oblique and distance in space
The perpendicular AB is drawn from point A to plane α; the segment AC to another point C of the plane is an oblique and BC is the projection of the oblique. In right triangle ABC, AC is the hypotenuse, so the perpendicular is always shorter than any oblique. The distance from a point to a plane is the length of the perpendicular. Among obliques from one point, the one with the longer projection is longer, and obliques with equal projections are equal; AC² = AB² + BC². All points of a line parallel to a plane are equally far from it, so that common distance is the distance from the line to the plane; the distance between parallel planes is the distance from any point of one to the other. Two skew lines have a unique common perpendicular; its length is the distance between the lines, which also equals the distance from the first line to the plane through the second line parallel to the first.
The floor and ceiling of a room model parallel planes: measure the distance between them at two different places with a tape measure (with an adult’s help) and check that the results are equal.