Postulates

Front 1

Unique Line Assumption:

Back 1

Through any two points, there is exactly one line.
Note: This doesn't apply to nodes or dots.

Front 2

Dimension Assumption:

Back 2

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.

Front 3

Number Line Assumption:

Back 3

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.

Front 4

Distance Assumption:

Back 4

On a number line, there is a unique distance between two points.

Front 5

If two points lie on a plane, the line containing them also lies on the plane.

Back 5

If two points lie on a plane, the line containing them also lies on the plane.

Front 6

Through three noncolinear points, there is exactly one plane.

Back 6

Through three noncolinear points, there is exactly one plane.

Front 7

If two different planes have a point in common, then their intersection is a line.

Back 7

If two different planes have a point in common, then their intersection is a line.