Math 100

Constructions

Steve Wilson

 

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.