Angle and chord properties
Many of the angle and chord properties of circles are inter-related and the order of treatment becomes important.
For example, from the theorem 'the angle at the centre is twice the angle at the circumference standing on the same chord' comes the theorem 'angles in the same segment are equal'. From there, the product of the intercepts of intersecting chords can be proven to be equal.
Presenting the theorems in an appropriate order allows students to apply knowledge of the earlier theorems to prove subsequent results. You can download a list of circle geometry theorems to use in your classroom.
Provide your students with opportunities to make conjectures and then prove theorems. They can explore, predict and confirm through interacting with dynamic diagrams. This will also strengthen their ability to visualise angle relationships and frequently prompts further conjecture.
Students will need:
- extensive practice in locating and evaluating angles
- guided experience in writing a proof.