# Geometry

## Points, Lines, And Planes

Points, lines, and planes are primitive terms; no attempt is made to define them. They do have properties, however, which can be explicitly described. Among the most important of these properties are the following:

Two distinct points determine exactly one line. That line is the shortest path between the two points. Bricklayers use these properties when they stretch a string from corner to corner to guide them in laying bricks.

Two points also determine a ray, a segment, and a **distance**, symbolized for points A and B by AB (or BA when B is the endpoint), AB, and AB respectively. (Some authors use AB to symbolize all of these, leaving it to the reader to know which is meant.) Three non-collinear points determine one and only one **plane**.

The photographer's tripod exploits this to hold the camera steady; the chair on an uneven floor **rocks** back and forth between two different planes determined by two different combinations of the four legs.

If two points of a line lie in a plane, the entire line lies in the plane. It is this property which makes the plane "flat." Two distinct lines intersect in at most one point; two distinct planes intersect in at most one line. If two *coplanar* lines do not intersect, they are **parallel**. Two lines which are not coplanar cannot intersect and are called "skew" lines. Two planes which do not intersect are parallel.

A line which does not lie in a plane either intersects that plane in a single point, or is parallel to the plane.

## Additional topics

Science EncyclopediaScience & Philosophy: *Gastrula* to *Glow discharge*Geometry - Proof, Constructions, Points, Lines, And Planes, Angles, Parallel Lines And Planes