Circle theorems lesson 4

A complete lesson on the theorem that opposite angles in a cyclic quadrilateral sum to 180 degrees. Assumes that pupils have already met the theorems that the angle at the centre is twice the angle at the circumference, the angle in a semicircle is 90, and angles in the same segment are equal. See my other resources for lessons on these theorems.

Activities included:

Starter:
Some basics recap questions on the theorems already covered.

Main:

• An animation to define a cyclic quadrilateral, followed by a quick question for pupils, where they decide whether or not diagrams contain cyclic quadrilaterals.
• An example where the angle at the centre theorem is used to find an opposite angle in a cyclic quadrilateral, followed by a set of three similar questions for pupils to do. They are then guided to observe that the opposite angles sum to 180 degrees.
• A quick proof using a very similar method to the one pupils have just used.
• A set of 8 examples that could be used as questions for pupils to try and discuss. These have a progression in difficulty, with the later ones incorporating other angle rules. I’ve also thrown in a few non-examples.
• A worksheet of similar questions for pupils to consolidate, followed by a second worksheet with a slightly different style of question, where pupils work out if given quadrilaterals are cyclic.
• A related extension task, where pupils try to decide if certain shapes are always, sometimes or never cyclic.

Plenary:
A slide showing all four theorems so far, and a chance for pupils to reflect on these and see how the angle at the centre theorem can be used to prove all of the rest.

Printable worksheets and answers included.

Please review if you buy as any feedback is appreciated!