Today we look again at Geometric Constructions, this time using more modern tools. 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 much 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 today we will focus on the free Geometry Calculator from GeoGebra.

GeoGebra’s online Geometry calculator

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).

## The Center of a Triangle

DISCUSSION: How do we find 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?

1. Bisect each angle
2. Center of the biggest possible circle inside the triangle (incenter)
3. Equidistant from each side
4. Connect the midpoint of each side to the opposite vertex (centroid)
5. Equidistant from each vertex
6. Center of the smallest possible circle containing the triangle (circumcenter)
7. Perpendicular bisectors of each side
8. Altitude of each side (orthocenter)