Which statement is an example of an axiom?

• A. The sum of the angles in a triangle equals 180 degrees.
• B. There are 360 degrees in a full circle.
• C. The diagonals of a rectangle bisect each other.
• D. The square root of 2 is irrational.

Answer: (B)

Axioms are statements we take as true without proof to serve as the starting point of a theory. The idea that a full circle has 360 degrees is such a foundational convention: it defines how we measure angles and isn’t something proven from other facts. It’s accepted upfront to fix the unit of angle measurement, so it acts as an axiom in this setting.

The other statements are things derived from those starting ideas. The sum of the angles in a triangle being 180 degrees can be proven using basic geometric facts about parallel lines. The diagonals of a rectangle bisect each other follows from the properties of parallelograms. The square root of 2 being irrational is shown by a contradiction argument. So they’re not taken as given; they’re proven within the system.