In mathematics, we propose conjectures, statements based on observation, which we then must prove.  We prove conjectures using axioms, postulates, and theorems.  Once a conjecture is proven, it becomes a theorem, which can then be used to prove other conjectures. 

Two types of reasoning we can use to prove conjectures is inductive reasoning and deductive reasoning.

Proofs can be presented in different ways, including two-column proofs and paragraph proofs.

Conjectures, axioms, postulates and theorems are often the form of conditional statements.  A conditional statement is a logical statements that has a hypothesis and conclusion.  A common type of conditional statement is an "IF-THEN" statement.