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7 Cards in this Set

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Unique Line Assumption:
Through any two points, there is exactly one line.
Note: This doesn't apply to nodes or dots.
Dimension Assumption:
Given a line in a plane, there exists a point in the plane not on that line. Given a plane in space, there exists a line or a point in space not on that plane.
Number Line Assumption:
Every line is a set of points that can be put into a one-to-one correspondence with real numbers, with any point on it corresponding to zero and any other point corresponding to one.
Note: This doesn't apply to nodes or dots. This was once called the Ruler Postulate.
Distance Assumption:
On a number line, there is a unique distance between two points.
If two points lie on a plane, the line containing them also lies on the plane.
If two points lie on a plane, the line containing them also lies on the plane.
Through three noncolinear points, there is exactly one plane.
Through three noncolinear points, there is exactly one plane.
If two different planes have a point in common, then their intersection is a line.
If two different planes have a point in common, then their intersection is a line.