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Basic Assumptions of Point-Line-Plane Postulate

Postulates can be defined as statements that are assumed and accepted to be true without proof. Postulates are used to explain undefined terms and also to start as a starting point for proving other statements.

The point-line-plane postulate in geometry is a collection of three assumptions that are the basis for Euclidean geometry in three or more dimensions.

The three main assumptions of Point-Line-Plane Postulate can be defined as follows:

Unique Line Assumption - Through any two points, there is exactly one line.

Number Line Assumption - Every line is a set of points that can be put into a one-to-one correspondence with the real numbers, with any point on it corresponding to 0 and any other point corresponding to 1.

Dimension Assumption - Given a line in a plane, there is at least one point in the plane that is not on the line.

Given a plane in a space, there is at least one point in space that is not in the plane.


 
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