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.

- Two points
determine a line
segment.

- A line segment can be extended indefinitely along a line.
- A circle can be drawn with a center and any radius.
- All right angles are congruent.
- If two lines are cut by a transversal, and the interior angles on the same side of the transversal have a total measure of less than 180 degrees, then the lines will intersect on that side of the transversal.

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