# Theorems on cyclic quadrilaterals

From Karnataka Open Educational Resources

### Objectives

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

Converse theorems:

- Suppose a quadrilateral is such that the sum of two opposite angles is a straight angle, them the quadrilateral is cyclic.
- 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

- A cyclic quadrilateral and its properties.
- The linear pair and exterior angle theorem.
- 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:

- The teacher can project the geogebra file and prove the theorems.

- Developmental Questions:

- How many angles does a cyclic quadrilateral have ?
- Name the opposite angles of it.
- Name the minor arc.
- Recall the angle -arc theorem.
- What is the total angle at the centre of a circle ?
- Name the angles at the centre of the circle.
- What is the sum of those two angles ?
- How can you show that