Ruler and Compass Constructions

A typical activity in Geometry classes is to do ruler and compass constructions. In such a construction one is allowed to draw a line segment defined by two points and to draw a circular arc defined by the center of a circle and a point on the circle. One of the frequently unstated rules is that you must also justify why the points, lines and curves constructed have the properties you desire of them. Thus for example the "construction of the perpendicular bisector of a line segment" involves both given the steps in the construction and justifying why the line produced must be the desired bisector.

This page links to a series of applets constructed with GeoGebra that walks through classical ruler and compass constructions.
Constructions are allowed to use a technique from a previous construction.

The construction of a line bisecting an angle
The construction of the bisector of a line segment
The construction of a line perpendicular to a segment from a point on the segment
The construction of a line perpendicular to a segment from a point not on the segment
The construction a line through a given point parallel to a given line
The construction of a segment that is an integer multiple of the length of a segment
The division of a segment in an integer number of pieces, all of the same length

GeoGebra is a GNUed software package for mathematics visualization. The home for the applications is http://www.geogebra.at.

Return to the GeoGebra Applet page.
Return to the Applets for courses below calculus page.
Return to the Calculus Applet page.

Last updated By Mike May, S.J., September 11, 2008.