Circle theorems lesson 3

A complete lesson on the theorem that angles in the same segment are equal. I always teach the theorem that the angle at the centre is twice the angle at the circumference first (see my other resources for a lesson on that theorem), as it can be used to easily prove the same segment theorem.

Activities included:

Some basic questions on the theorems that the angle at the centre is twice the angle at the circumference, and that the angle in a semi-circle is 90 degrees, to check pupils remember them.


  • Slides to show what a chord, major segment and minor segment are, and to show what it means to say that two angles are in the same segment. This is followed up by instructions for pupils to construct the usual diagram for this theorem, to further consolidate their understanding of the terminology and get them to investigate what happens to the angle.
  • A ‘no words’ proof of the theorem, using the theorem that the angle at the centre is twice the angle at the circumference.
  • Missing angle examples of the theorem, that could be used as questions for pupils to try. These include more interesting variations that incorporate other angle rules.
  • A set of similar questions with a progression in difficulty, for pupils to consolidate.
  • Two extension questions.

A final set of six diagrams, where pupils have to decide if two angles match, either because of the theorem learnt in the lesson or because of another angle rule.

Printable worksheets and answers included.

Please do review if you buy as any feedback is greatly appreciated!

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  • 3-angles-in-the-same-segment.pptx

About this resource


Created: May 8, 2018

Updated: Mar 5, 2019

Whole lesson

pptx, 349 KB


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