# Cyclic quadrilateral

From Karnataka Open Educational Resources

A quadrilateral ABCD is called cyclic if all four vertices of it lie on a circle.In a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.If the sum of a pair of opposite angles of a quadrilateral is 180, the quadrilateral is cyclic.In a cyclic quadrilateral the exterior angle is equal to interior opposite angle.

### Objectives

Understanding cyclic quadrilaterals

Relation between angles of a cyclic quadrilateral.

### Estimated Time

10 minutes

### Prerequisites/Instructions, prior preparations, if any

Circle and quadrilaterals should have been introduced.

### Materials/ Resources needed

Digital : Laptop, geogebra file, projector and a pointer.

Geogebra file: Cyclic quadrilateral.ggb

Download this geogebra file from this link.

### Process (How to do the activity)

- The teacher can recall the concept of a circle, quadrilateral, circumcircle.
- Can explain a cyclic quadrilateral and show the geogebra applet.
- Move points, the vertices of the quadrilateral and let the students observe the sum of opposite interior angles.

- Developmental Questions:

- What two figures do you see in the figure ?
- Name the vertices of the quadrilateral.
- Where are all the 4 vertices situated ?
- Name the opposite interior angles of the quadrilateral.
- What do you observe about them.

- Evaluation:

- Compare the cyclic quadrilateral to circumcircle.

- Question Corner

- Can all quadrilaterals be cyclic ?
- What are the necessary conditions for a quadrilateral to be cyclic ?