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.
