• A definition (or formal definition) is a statement of the "precise" meaning of a word or word group.
• A theorem is a statement (rule) that has been proven true using facts, operations and other rules that are known to be true. These are usually the "big" rules of geometry. A short theorem referring to a "lesser" rule is called a lemma.
• A corollary is a follow-up to an existing proven theorem. Corollaries are off-shoots of a theorem that require little or no further proof.
• A postulate (or axiom) is a statement (rule) that is taken to be true without proof based upon geometric principles. Postulates are often simply "common sense" ideas, such as "Through any two points, there is exactly one straight line."
Note: Euclid derived many of the rules for geometry starting with a series of definitions and only five postulates.
• A property is a quality or characteristic belonging to something.
For example, the real numbers have the associative, commutative and distributive properties.
