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Axioms and Postulates

Two of the most important building blocks of geometric proofs are axioms and postulates. In the following lessons, we'll study some of the most basic ones so that they will be available to you as you attempt geometric proofs.

Axioms and postulates are essentially the same thing: mathematical truths that are accepted without proof. Their role is very similar to that of undefined terms: they lay a foundation for the study of more complicated geometry. Axioms are generally statements made about real numbers. Sometimes they are called algebraic postulates. Often what they say about real numbers holds true for geometric figures, and since real numbers are an important part of geometry when it comes to measuring figures, axioms are very useful. Postulates are generally more geometry-oriented. They are statements about geometric figures and relationships between different geometric figures. We've already studied some, such as the parallel postulate. In the following lessons we'll formally outline some of the most important, but certainly not all, of the axioms and postulates that one can use when writing a geometric proof.