## Constructions

The point of this page is to list some constructions which are
possible in the real Cartesian coordinate plane. The proofs that the
first seven constructions are possible are found in the
Analytic Foundations of
Geometry website.

1.
Given two points, there is a unique line that joins them.

2.
Given two lines which are not parallel, there is a unique point where
they intersect.

3. Given a
line and a point not on the line, there is a unique line through the
point parallel to the line

4. Given a
point and a line, there is a unique line through the point
perpendicular to the line.

5.
Given two points, there is a point which is halfway between them on
the line segment joining the two points.

6. Given an
angle, there is a line through the vertex of the angle which bisects
it.

7.
Given a point and a distance, there is a unique circle centered at
the point having the given distance as its radius.

8.
Given a circle and a point outside the circle, there are two lines
through the point tangent to the circle.