Basic Building Blocks of Geometry

Geometry is based on a set of givens and uses deductive logic, called "proof," to establish conclusions.  The "givens" are definitions and/or postulates, and the "conclusions" are called theorems or corollaries.  (A "corollary" is a result that follows directly from a "theorem" and is easy to prove.  It is like a "mini-theorem.")

Some terms in geometry are classified as "undefined" or "primitive."  Euclid tried to define all terms he used, but not everything can be defined without going around in circles.  Today we accept certain concepts as "primitive" and do not attempt to define them.  The most basic are the terms point, line, plane, and space.  We use postulates to give them meaning.  Some of these postulates are:

1. For any two points, there is exactly one line containing them.
2. Every line contains at least two points.
3. Every plane contains at least three points not all on the same line.
4. Space contains at least four points not all in the same plane.
5. If a plane contains two points of a line, then that plane contains the whole line.
6. If a line intersects a plane that does not contain it, then it intersects the plane in exactly one point.
7. Any three points lie in at least one plane, and any three points not on the same line lie in exactly one plane.
8. If two planes intersect, their intersection is a line.

 

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