Theorems on cyclic quadrilaterals

Objectives

 * 1) Both pairs of opposite angles of a cyclic quadrilateral are supplementary.
 * 2) When one side of a cyclic quadrilateral is produced, the exterior angle so formed is equal to the interior opposite angle.

Converse theorems:
 * 1) Suppose a quadrilateral is such that the sum of two opposite angles is a straight angle, them the quadrilateral is cyclic.
 * 2) If the exterior angle of a quadrilateral is equal to the interior opposite angle, then the quadrilateral is cyclic.

Estimated Time
40 minutes

Prerequisites/Instructions, prior preparations, if any
Laptop, geogebra file, projector and a pointer

Materials/ Resources needed
This geogebra file was done by ITfC-Edu-Team.
 * 1) A cyclic quadrilateral and its properties.
 * 2) The linear pair and exterior angle theorem.
 * 3) The circle theorem (Angle at centre = double the angle at the circumference)

Process (How to do the activity)

 * Process:
 * 1) The teacher can project the geogebra file and prove the theorems.
 * Developmental Questions:
 * 1) How many angles does a cyclic quadrilateral have ?
 * 2) Name the opposite angles of it.
 * 3) Name the minor arc.
 * 4) Recall the angle -arc theorem.
 * 5) What is the total angle at the centre of a circle ?
 * 6) Name the angles at the centre of the circle.
 * 7) What is the sum of those two angles ?
 * 8) How can you show that