Circle geometry, proofs and dynamic geometry explorations with Desmos/ Geogebra

 Here are resources for four guided lessons using free, dynamic geometry software online -- either Desmos or Geogebra. These circle geometry theorems are currently included in the BC Geometry 12 curriculum, though they were in the Math 11 precalculus curriculum for many years. (If your school is not offering Geometry 12, these are some very interesting geometric ideas that could be introduced as an enrichment topic in the senior year classes!)

Overview and lesson one (retyped)
Lesson 1 again (scanned version)
Lesson 2 (scanned)
Lesson 3 (scanned)
Lesson 4 (scanned)
Older textbook deductive proofs (scanned, somewhat blurry)

In the olden days, students used to doing geometry with pencil, compass, straightedge and paper, but from the 1990s on,  many online dynamic (as opposed to static) geometry tools became available. Geometer's Sketchpad, Cabri, Cinderella and many more are listed on a Wikipedia page here.

By far the most popular of these is now Geogebra, as it is free, open-source, and contains many lesson ideas developed by and for teachers. Take some time to look at Geogebra and experiment a bit with it.

Desmos is also taking on many similar functions to Geogebra, and is also free and available to students and teachers. You will likely use Desmos and/or Geogebra with your classes


What are your thoughts on these guided geometry experiences? How do you feel they relate to more formal deductive proofs? Do you feel that these 'prove' the theorems?

In thinking this through, please refer to John Mason's three levels of proofs --
1) Prove it to yourself,
2) Prove it to a friend or ally,
3) Prove it to a sceptic.

Here is an excellent short article by John Mason on this topic, for your reference!