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:

• 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.
Line - has no thickness or width. It does have length, and the length extends infinitely in both directions, so its measure is infinite. Point – It holds location and has no thickness, length or width.  It has no measure in any direction.
• 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.