# 5 Basic Theorems & 5 Basic Postulates

xenopigu's version from 2016-01-27 06:25

## 5 Basic Postulates of Undefined Terms

a. Point - Existence Postulatespace contains at least four non-coplanar, noncollinear points
b. Point - Existence Postulatea plane contains at least three noncollinear points
c. Point - Existence Postulatea line contains at least two points
Line Intersection Postulatefor any two points there is exactly one line that contains both points
Plane Postulateany three noncollinear points lie in exactly one plane
Flat Plane Postulateif two parts are contained in the plane, then the line joining these points are contained in the plane
Plane Intersection Postulateif two planes intersect, then their intersection is a line

## 4 Basic Theorems of Undefined Terms

Line - Intersection TheoremIf two lines intersect, then their intersection is exactly one point
Line - Plane Intersection TheoremIf a line intersects a plane not containing it then their intersection is exactly one point
Line - Point TheoremGiven a line and a point not on the line, there is exactly one point that uses them
Line - Plane TheoremGiven two intersecting lines, there is exactly one plane that contains the two lines