Geometry Essential Questions

While there are a lot of individual things that are very fun and exciting about Geometry to teach, I have boiled my Geometry class down to five essential questions. These are at the heart of what I want my students to know when they leave the class. We still work on a lot of traditional geometry, but ultimately it must serve the following five questions.

1. What makes a logical argument?
2. Why is the notion of equivalence important?
3. What is important about knowing objects are similar?
4. What mathematical facts are important to know?
5. When does algebra help us understand geometry, and when does geometry help us understand algebra?

I have told my students that they have free rein to ask me, whenever we are working on something, where what we are doing fits one (or more) of the five questions. If I cannot answer that, then we stop doing it.