A postulate is an obvious geometric truth that is accepted without proof.  Postulates are assumptions that do not have counterexamples.

Some common and widely accepted assumptions (postulates) that are not mathematical in origin are:

• Money can’t buy happiness.
• All men are created equal.
• Knowledge is superior to ignorance.

The Properties of Algebra are also called the Postulates of Algebra and are used in geometry proofs.

#### Postulates of Equality

• Reflexive Property of Equality: a = a
• Symmetric Property of Equality: if a = b, then b = a
• Transitive Property of Equality: if a = b and b = c, then a = c

#### Postulates of Operations

• Commutative Property of Addition: a + b = b + a
• Commutative Property of Multiplication: a * b = b * a
• Associative Property of Addition:  (a + b) + c = a + (b + c)
• Associative Property of Multiplication: (a * b) * c = a * (b * c)
• Distributive Property: a * (b + c) = a * b + a * c and vice versa

Euclid based his study of geometry on the following postulates.  He accepted these statements to be true without proof.

Postulates serve as the starting points from which theorems are logically derived.