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.
Understanding cyclic quadrilaterals
Relation between angles of a cyclic quadrilateral.
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.
- Compare the cyclic quadrilateral to circumcircle.
- Question Corner
- Can all quadrilaterals be cyclic ?
- What are the necessary conditions for a quadrilateral to be cyclic ?