Math 150

Constructions

Steve Wilson

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.