Question

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.

Answer 1

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". 

Answer 2

Answer with explanation:

This can be explained by taking the example, when you stitch a cloth , you need fabric.Fabric are made from threads and threads are made from yarn.So, yarn is an Axiom while stitching a fabric.

So, Axioms are considered as yarn , from which theorems are derived.

You must be thinking from where these yarns came, from trees and from where these trees came,nature built it.

So, Nature has given us clues with the help of which we derived Mathematical axioms and then humans for their purpose with the help of these Axioms proved theorem for the welfare of Humans.