Cyclic Quadrilaterals

Opposite angles add to 180°

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A cyclic quadrilateral has all four vertices on one circle.
• Its opposite angles add up to 180°, and conversely.
• Rectangles are always cyclic. Non-square rhombuses never are.

Steps

1. Four points on a circle
2. Find the angle
3. An exterior angle
4. Same arc, same angle
5. Ptolemy’s theorem
6. Which shapes are cyclic?