Theorems, Postulates, and Definitions

In Unit 1, you were introduced to the concepts of theorems, postulates, and definitions. You also learned about the father of geometry, Euclid. You will now learn more about them in depth.

In order to have theorems, you need a starting point. We use definitions to make sense of the elements of geometry. We define that a point is a fixed location in space with no dimension. We also define a ray as half of a line with an initial point and an endpoint. You will learn the definitions that you need as you go through this course.

Recall that postulates are statements that are accepted as true which are not proven. Again, it is necessary to have a few starting rules about how our defined elements interact in order to discover other theorems. Postulates can also be called axioms.

Euclid originally had 5 postulates on which he based the rest of plane geometry. They are:

Theorems are statements that can be proven using definitions, postulates, and other proven theorems.

The Pythagorean Theorem is an example of a theorem that you may have studied in one of your previous math classes, and that we will use later in this course.