Over the course of the SparkNotes in Geometry 1 and 2, we have already been introduced to some postulates. In this section we'll review those, as well as go over some of the most important postulates for writing proofs.
A number of postulates have to do with lines. Some are listed here.
Other postulates have to do with measurements. Here are some.
The three methods discussed for proving the congruence of triangles are all postulates. These are the SSS, SAS, and ASA postulates. There is no formal way to prove that they hold true, but they are accepted as valid methods for proving the congruence of triangles.
One final postulate has been assumed all along in the study of geometry: a given geometric figure can be moved from one place to another without changing its size or shape. In this text, (other than in this brief instance) we have not and will not discuss the coordinate plane. The coordinate plane is a system in which numbers are assigned to different locations within the plane, thus determining the exact location of geometric figures. In this text we simply study the figure as it exists anywhere, so it follows that it can be moved without being changed (as far as size and shape are concerned). The postulate simply states formally that the size and shape of a geometric figure do not change when it is moved.
With an understanding of these postulates, as well as the axioms discussed in the previous lessons, we're now ready to attempt some formal proofs.