As we saw last time, software can easily replicate the capabilities of the ruler and compass – but can also be used to apply those techniques without the same kind of human error that physical tools can generate. More complicated constructions become easier to carry out, and the resulting figures can be manipulated while preserving each element of the construction.
There are a number of geometry tools online, but we will continue to focus on the free Geometry Calculator from GeoGebra. This powerful free tool can be used for all kinds of geometry constructions and demonstrations (no account required, though you can create a free account if you want to save your work). Last time we used a limited version with basic ruler and compass tools only. The full version (link below) has many more tools available, which allow you to carry out complex ruler-and-compass constructions like bisecting an angle or finding the midpoint of a segment with the click of a button.
GeoGebra’s online Geometry calculator
- GeoGebra Geometry resources.
- GeoGebra Geometry App: Beginner Tutorials with Lesson Ideas. This series of pages serves a good introduction to the GeoGebra Geometry app.
The Center of a Triangle
DISCUSSION:
How do we find the center of a triangle?
Let’s talk about some different ideas of how to find the center – thinking in terms of geometric constructions.
Construct some of the following in GeoGebra. What do you notice?
- Bisect each angle
- Center of the biggest possible circle inside the triangle (incenter)
- Equidistant from each side
- Connect the midpoint of each side to the opposite vertex (centroid)
- Equidistant from each vertex
- Center of the smallest possible circle containing the triangle (circumcenter)
- Perpendicular bisectors of each side
- Altitude of each side (orthocenter)
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