What is Postulates?

Introduction:

             A statement whose validity is accepted without proof is called a postulate.
In addition to point, line plane etc, it is also necessary to start with certain other basic statements that are accepted without proof. In Basic geometry these are called postulates.
A postulate, though itself is an unproved statement, can be cited as a reason to support a step in a proof. Postulates are just like axioms in arithmetic sequence and algebra, that they are accepted without proof.

Some of the postulates we use often are:

• The line containing any two points in a plane lies wholly in that plane.
• An angle has only one and only one bisector.
• Through any point outside a line, one and only one perpendicular lines can be drawn to the given line.
• A segment has one and only one mid point.
• Linear pair postulate: If a ray stands on a line, then the sum of the two adjacent angles so formed is 180^o.

Activity 1:

Mark two distinct points A and B on the plane of your note book. Can you draw a line passing through A and B?

By experience we find that we can draw only one line through two distinct points A and B.
Hence "Given any two distinct points in a plane, there exists one and only line containing them".
This is a self-evident truth. Hence it is a postulate.

Hope you liked the above explanation. Please leave your comments, if you have any doubts.