Question

What is the difference between a theorem and an axiom?

Answer 1

An axiom is a basic fact that is taken for granted without proof.
Examples:
i) Halves of equals are equal.
ii) The whole is greater than each of its parts.

Theorem: A statement that requires proof is called theorem.
Examples:
i) The sum of all the angles around a point is ${360}^{\circ }$.
ii) The sum of all the angles of triangle is ${180}^{\circ }$.