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

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)

This geogebra file was done by ITfC-Edu-Team.

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