Key Concepts: Postulates and Paragraph Proofs

Postulates (Axioms)

A postulate is a statement accepted as true without proof. Postulates serve as the foundation for building theorems through logical reasoning.

Theorems

A theorem is a statement that has been proven true using postulates, definitions, and previously proven theorems.

Paragraph Proof

A paragraph proof (informal proof) presents a logical argument in paragraph form, where each statement is backed by a reason (definition, postulate, or theorem).

• State what is given and what you need to prove.
• Write a series of statements, each justified by a reason.
• Conclude with what you set out to prove.