Continuing my incorporation of GeoGebra into my Geometry curriculum (read about my introduction of GeoGebra here), we will start slow and simple. We are learning the basics of proof, and GeoGebra is a great tool for sparking discussion of what we might want to prove.
Example: one of the first exercises every Geometry student does is to prove that vertical angles are congruent. Instead of having them look at static pictures of vertical angles, each of my students will construct two intersecting lines, measure the angles formed, and look for a relationship. They should quickly see that the vertical angles are congruent no matter how much they move the lines around. Hopefully, they will then wonder why is that always the case. And that’s where proof comes in: if they can write a proof using variables, then they have proven it for all cases, not just the one they’re looking at.
Because it is dynamic, GeoGebra is a great tool for generating lots of conjectures. Geometry is the means we use for formally proving them.