Now these postulates are necessary to give the proper meaning to the undefined terms. In particular, they captivate the notions of "straightness" and "flatness." Thus, lines are "straight" and planes are "flat." Intuitively we think of a point as a location. It has no width or thickness. A line separates a plane into two halves and has no width, and a plane separates space into two halves and has no thickness.
Since the concepts of "being on the same line" and "being in the same plane" are important in geometry, we use definitions to simplify them:
1. Definition: Two or more points are collinear if they all lie on the same line.
2. Definition: Two or more points are coplanar if they all lie in the same plane.
These definitions can be used to shorten postulates 3, 4 and 7:
3. Every plane contains at least three noncollinear points.
4. Space contains at least four noncoplanar points.
7. Any three points lie in at least one plane, and any three noncollinear points lie in exactly one plane.
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Date last modified: September 8, 2008.