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The opposite angles of a cyclic quadrilateral sum to 180°

I can derive and use the theorem: the opposite angles of a cyclic quadrilateral sum to 180°.

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Year 10

The opposite angles of a cyclic quadrilateral sum to 180°

I can derive and use the theorem: the opposite angles of a cyclic quadrilateral sum to 180°.

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Key learning points

A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments
Theorems can be thought of as puzzles to solve, you are showing how to find a result
In order to use this theorem, you may need to draw a diagram or add more information to an existing one

Keywords

Cyclic quadrilateral - A cyclic quadrilateral is a quadrilateral where all four of its vertices lie on a single circle.

Common misconception

Pupils may conflate cyclic quadrilaterals with cases of "the angle at the centre of a circle is twice the angle at the circumference" theorem, when the angle at the centre is a reflex angle.

While the two diagrams may look similar at a glance, pay extra attention to whether all four points of the quadrilateral are on the circumference or if one of the points is in the centre.

The lesson demonstrates how this circle theorem could be explored practically by using a circular geoboard and using dynamic geometry software. Pupils may wish to explore these further for themselves.

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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).