Question

What is the difference between lemma and axiom?

Answer 1

Axiom
Generally accepted and recognized as truth. It's self-evident without proof. These are the basic building blocks from which all theorems are proved

Example : 2+2 = 4

Sun rise in the east

These expression are an universally accepted truth

Lemma

A lemma is some statement that can be shown to be true, starting from some previously accepted statements, that is used to show that some other statement or statements are true.

Lemma

(This is sometimes called the "Angle in the Semicircle Theorem", but it’s really just a Lemma to the "Angle at the Center Theorem")

In the special case where the central angle forms a diameter of the circle:

2a° = 180° , so a° = 90°

So an angle inscribed in a semicircle is always a right angle.

(That was a "small" result, so it is a Lemma.)