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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
GM6-4
New NZC (2026)
NZC26-P4-GEO-SHP-P-Y9-01
Resources
- CorbettMaths - Cyclic Quadrilateral Proof video
- CorbettMaths - Circle Theorems practice questions (incl. cyclic quadrilaterals)Questions PDF · Answers
- Dr Austin Maths - Cyclic Quadrilaterals Practice GridQuestions PDF · Answers
Terminology
- Cyclic quadrilateral
- Opposite angles
- Circumscribed circle
- Exterior angle
- Interior angle
- Supplementary angles
Task goals
- Identify a cyclic quadrilateral as a four-sided shape with every vertex on a circle.
- State and apply the cyclic quadrilateral theorem (opposite interior angles sum to 180 degrees) to find one missing angle.
- Apply the exterior-angle property of a cyclic quadrilateral (an exterior angle equals the interior opposite angle) to find a missing angle.
- Set up and solve an algebraic equation from two opposite angles given as expressions to find an unknown variable.
- Combine the cyclic quadrilateral property with other circle theorems in a single diagram to solve multi-step angle problems, explaining which theorem justifies each step.
Where this fits
What leads into this objective, and where it goes next.
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Cyclic Quadrilaterals
Also under GM6-4:
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.