Here is the correct matching of each term to its definition:

1. Axiom - a given definition assumed to be true
2. Proof - a logical argument showing that a theorem is true
3. Theorem - a statement that requires proof

Would you like more details or have any questions? Here are some related questions for further exploration:

1. What are some examples of commonly accepted axioms in mathematics?
2. How does a proof differ from a conjecture?
3. What is the difference between a theorem and a lemma?
4. Can a proof be both inductive and deductive?
5. What role do axioms play in developing mathematical theories?
6. How are theorems used to build more complex mathematical concepts?
7. What is an example of a famous theorem and its proof?
8. How do mathematicians ensure that a proof is rigorous and valid?

Tip: When working on proofs, always start by understanding the axioms and definitions involved, as they are the foundation of any logical argument.