Cyclic quadrilateral

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

Process (How to do the activity)

 * 1) The teacher can recall the concept of a circle, quadrilateral, circumcircle.
 * 2) Can explain a cyclic quadrilateral and show the geogebra applet.
 * 3) Move points, the vertices of the quadrilateral and let the students observe the sum of opposite interior angles.
 * Developmental Questions:
 * 1) What two figures do you see in the figure ?
 * 2) Name the vertices of the quadrilateral.
 * 3) Where are all the 4 vertices situated ?
 * 4) Name the opposite interior angles of the quadrilateral.
 * 5) What do you observe about them.
 * Evaluation:
 * 1) Compare the cyclic quadrilateral to circumcircle.
 * Question Corner
 * 1) Can all quadrilaterals be cyclic ?
 * 2) What are the necessary conditions for a quadrilateral to be cyclic ?