Alternate Segment Theorem
Select points A, B and C and move them round the circle.
What do you notice about the size of the angles?
What can you say about Angles in Alternate Segments?
Why is it called the Alternate Segment Theorem?
Can you prove the result?
Ideas for Teachers
Use this Activity as a homework, where the students must come up with a conjecture regarding the Alternate Segment Theorem. 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.
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.
Use this Activity as a homework, where the students must come up with a conjecture regarding the Alternate Segment Theorem. 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.
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.

alternate_segment.agg  
File Size:  16 kb 
File Type:  agg 