Question

What is a postulate and a theorem?

Answer 1

Postulate is something that is universally accepted.

For instance, 3 x 2 = 2 x 3 is something that is universally accepted (also known as an axiom). You don't need to PROVE this fact.
Another example is 5 x 1 = 5. This doesn't need to be proven; it is automatically accepted and you need these postulates to construct mathematical arguments.


Something that needs to be PROVEN is a THEOREM.
An example of a theorem:

Given a right triangle of sides a,b, and c, where c is the hypotenuse and and a and b are the legs,
a^2 + b^2 = c^2.

If the legs of a triangle are 3 and 4, you know for sure that the hypotenuse is 5. But this is obviously not a postulate, because it requires a proof (a mathematical argument).