# Cyclic Quadrilaterals

*Keywords:*

AO elaboration and other teaching resources

The purpose of this activity is to engage students in considering geometric properties when categorising shapes.

This activity ideally follows exploration and learning in the following areas.

Click to show example questions for each heading

To solve this problem, the students may sketch, construct or explore with number. The approach should be chosen in sympathy with their skills and preferred method of solution. Choices of blank or gridded paper, along with maths construction tools should be made available.

A cyclic quadrilateral is a four sided shape which has the following properties:

- All four vertices lie on the circumference of a single circle.
- Opposite interior angles sum to 180°.

Which of the following **cannot** be a cyclic quadrilateral?

- a square
- a rectangle that is not a square
- a rhombus that is not a square
- a kite that is not a rhombus
- a parallelogram that is not a rhombus
- a trapezium, that is not a parallelogram
- an arrowhead.

### The procedural approach (show more)

- The student is able to use geometric reasoning and/or exploration, with guidance, to solve a problem.

### The conceptual approach (show more)

- The student is able to use geometric reasoning and/or exploration, with guidance, to solve a problem.

Attachment | Size |
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CyclicQuadrilaterals_full.pdf | 641.38 KB |

CyclicQuadrilaterals_conceptual.pdf | 386.67 KB |

CyclicQuadrilaterals_procedural.pdf | 386.27 KB |