Circle theorems lesson 2

A complete lesson on the theorem that the angle in a semicircle is 90 degrees. 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 semicircle theorem.

Activities included:

Starter:
Some basic questions on the theorem that the angle at the centre is twice the angle at the circumference, to check pupils remember it.

Main:

• Examples and non-examples of the semicircle theorem, that could be used as questions for pupils to try. These include more interesting variations like using Pythagoras’ theorem or incorporating other angle rules.
• A set of questions with a progression in difficulty. These deliberately include a few questions that can’t be done, to focus pupils’ attention on the key features of diagrams.
• An extension task prompt for pupils to create their own questions using the two theorems already encountered.

Plenary:
Three discussion questions to promote deeper thinking, the first looking at alternative methods for one of the questions from the worksheet, the next considering whether a given line is a diameter, the third considering whether given diagrams show an acute, 90 degree or obtuse angle.

Printable worksheets and answers included.

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