Angles in a Semicircle
Select point A and move it round the circle.
Use the Animate function to set up an animation of point A around the circle.
What do you notice about the size of the angle? Select point B and move it around the circle. What can you say about the Angle in a Semicircle? Can you prove the result?
What do you notice about the size of the angle?
Select point B and move it around the circle.
What can you say about the Angle in a Semicircle?
Can you prove the result?
Use this Activity as a homework, where the students must come up with a conjecture regarding Angles in a Semicircle. Ensuring they are using the correct vocabulary here is essential.
As an extension task, you could ask the students to try and prove this result (having done the Angles at the Centre theorem, this should be fairly accessible for all).
An alternative approach, which is even more hands on, is to get them to make this in Autograph themselves. You could do this in two ways: show them this activity, asking them to reproduce it (will develop their understanding of Autograph and circles); use the worksheet provided which gives a step by step approach to creating it.
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A worksheet for students to work through which involves them creating the above activity using Autograph before doing the investigation.