Straightedge and Compass
Straightedge
Straightedge can be regarded as a ruler without any marking.
The following are exactly what a straightedge can do:
- Draw a unique straight line through two distinct points
- Extend a line segment arbitrarily far in both direction
![A straightedge](https://beta.geogebra.org/resource/nmZgfkAC/F5fFCsV50ReJ0Ov0/material-nmZgfkAC.png)
Compass
Compass is a V-shaped drawing tool with a sharp point on one arm and a pencil on another arm. The two arms are joined by a hinge so that the openings of the arms is adjustible.
Obviously, a compass is mainly used for constructing a circle centered at any given point with any given radius.
There are two types of compasses:
- Modern compass - We can keep the opening fixed when the compass leaves the plane and carry to another location for construction.
- Euclidean (or collapsible) compass - The compass "forgets" the width of the opening when the compass leaves the plane i.e. we cannot keep the opening fixed.
![A real compass](https://beta.geogebra.org/resource/Svhw3wSX/bLV8jwjj0Lx5CqSB/material-Svhw3wSX.png)
Geometric Constructions
We can use the following applet to simulate geometric constructions using straightedge and compass.