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Geogebra-constructing equilateral figures

Geogebra-constructing equilateral figures

Author: Christopher Danielson

To demonstrate some basic geometric functionality of GeoGebra for people familiar with compass-and-straightedge constructions.

A series of four videos demonstrates constructions in GeoGebra (an open-source dynamic geometry and algebra software).

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This packet gives a quick overview of some geometry features of GeoGebra, an open-source dynamic geometry and algebra software. In order to use the packet effectively, you should already have access to GeoGebra and know something about compass and straightedge constructions-especially of circles, equilateral triangles and rhombi.

The logic behind compass and straightedge constructions is the same logic that drives dynamic geometry software like GeoGebra. The idea is that we are focusing on the geometric properties of the figures we construct, not on what they look like, nor on their measurements. What GeoGebra adds to our experience is that these geometric properties are preserved as we change our diagram. So if we construct a rhombus correctly, we can change one side length and they all change because the relationships among the sides stay the same, even as the sides themselves change.

This principle will be demonstrated in the constructions you are about to view.

Constructing an equilateral triangle

This video shows the process of constructing an equilateral triangle using a given side length. Several basic tools in GeoGebra are demonstrated.

A few useful features

This video demonstrates a couple of nice tricks for making your construction look nicer. These tricks do not affect the geometric relationships in your construction; they just neaten things up a bit.

Constructing an equilateral quadrilateral (a rhombus)

This video demonstrates constructing a rhombus in GeoGebra.

Some final tidying

This video demonstrates a clever trick for tidying up one thing in the previous construction. It's an advanced technique.