Rules of Perspective

If PQ is a line segment in "real-life", then its perspective image P'Q' will also be a line segment, unless PQ is seen end-on (that is, unless PQ is orthogonal to the picture plane and directly opposite the viewer's eye), in which case the perspective image will just be a point.
Why?
If PQ is a line segment in "real-life" that lies in a plane parallel to the picture plane, then its perspective image P'Q' is parallel to PQ .
Why?
If two line segments PQ and RS are parallel in "real-life", and are also parallel to the picture plane, then their perspective images P'Q' and R'S' are parallel to each other.
Why?
(Restatement of Vanishing Point Theorem) If two or more lines in the real world are parallel to each other, but not to the picture plane, then they have the same vanishing point. To restate the obvious, the perspective images will not be parallel, and if extended, will intersect at the vanishing point.
Furthermore, if these lines are orthogonal to the picture plane, their vanishing point will be the point directly opposite the ideal viewing position ("the viewer's eye"). This vanishing point is called the primary vanishing point, or the principal vanishing point.

If instead, these lines lie in a plane parallel to the "floor", then their vanishing point will lie on the horizon line (the horizontal line through the primary vanishing point; i.e. through the point directly opposite the viewer's eye).

And finally, if they lie in a plane parallel to the "side walls", then their vanishing point will like on the vertical line through the primary vanishing point.
A shape that lies entirely in a plane parallel to the picture plane has a perspective image that is an undistorted miniature of the original. A shape that lies in any other plane will be distorted.
Why?

Next-using the rules of perspective to draw a cube

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