A thorough understanding of circle geometry is best achieved when students explore the relationships and see the results in a variety of situations.
- Construct accurately with pen-and-paper and then measure angles and lengths.
- Create dynamic diagrams which can be manipulated.
- Fold paper circles.
- Solve problems involving angle measurements.
Once students have a clear understanding of the theorems it is both mathematically sound and good teaching practice to prove the theorems using formal deductive geometry strategies.
From there, more complex problems can be posed which require the students to link the theorems.
Explore, predict, confirm
Dynamic circle diagrams help students visualise the theorems in various configurations. They can make predictions and confirm their ideas as they explore.