As you have read, axioms are mathematical statements that are assumed to be true and taken without proof. use complete sentences to describe why a proof would need to have axioms to build on.

A mathematical proof is an elaborate explanation of why something is true. It uses logic as its method and it proves that something is true. In order to be able to prove this, we need to have some previous facts from which we can deduce these new facts. These "old" facts which we assume to be true are called "Axioms".