Postulates are statements, which are accepted without proof. These are also called axioms.. These are self proving

A theorem is a statement, which requires a proof to establish its truth.

For Example, the following statements are axioms or postulates:

There is only one straight line joining any two distinct points

A line has length, but no width

Two straight lines, which are not parallel, intersect at one point.

If two parallel lines are cut by a transversal, then the pair of corresponding angles are congruent

Sum of the angles of a triangle is 180 degrees

Like wise, there are many such postulates, which one will come across while studying Geometry’ On the other hand following statements are theorems

Sum of the lengths of any two sides of a triangle is greater than the length of the third side

The median of a triangle meet at a point dividing them in the ratio 1:2

A line joining the middle points of any two sides of triangle, is parallel to the third side and equals half of the length of the third side.

These are illustrated in the figure on the next page,