What is the difference between a theorem and an axiom?

Question:

What is the difference between a theorem and an axiom?

Solution:

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 $180^{\circ}$.

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