Maths 2: Relationships of Points, Lines and Planes

Postulates and Theorems

Postulate 1
A line contains at least two distinct points. A plane contains at least three non-collinear points. Space contains at least four non-coplanar points.

Postulate 2
If two distinct points are given, then a unique line contains them.

Postulate 3
Through any two points there are infinitely many planes. Through any three points there is at least one plane. Through any three non-collinear points there is exactly one plane.

Postulate 4
If two points are in a plane, then the line that contains those points lie entirely in the plane.

Postulate 5
If two distinct planes intersect, then their intersection is a line.

Theorem 1.1
If two distinct lines intersect, then they intersect in exactly one point.

Theorem 1.2
If there is a line and a point not in the line, then there is exactly one plane that contains them.

Theorem 1.3
If two distinct lines intersect, then they lie in exactly one plane.