# Properties of cyclic quadrilateral

Jump to navigation
Jump to search

Relation between the angles of a cyclic quadrilateral are explored with this hand on activity.

### Objectives

- In a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.
- In a cyclic quadrilateral the exterior angle is equal to interior opposite angle

### Estimated Time

45 minutes

### Prerequisites/Instructions, prior preparations, if any

- Circles and quadrilaterals should have been covered.

### Materials/ Resources needed

Non digital: Coloured paper, pair if scissors, sketch pen, carbon paper, geometry box

This activity has been taken from the website http://mykhmsmathclass.blogspot.in/2007/11/class-ix-activity-16.html

### Process (How to do the activity)

Note: Refer the above geogebra file to understand the below mentioned labelling.,br>

- Draw a circle of any radius on a coloured paper and cut it.
- Paste the circle cut out on a rectangular sheet of paper.
- By paper folding get chords AB, BC, CD and DA in order.
- Draw AB, BC, CD & DA. A cyclic quadrilateral ABCD is obtained.
- Make a replica of cyclic quadrilateral ABCD using carbon paper.
- Cut the replica into 4 parts such that each part contains one angle .
- Draw a straight line on a paper.
- Place angle BAD and angle BCD adjacent to each other on the straight line.Write the observation.
- Place angle ABC and angle ADC adjacent to each other on the straight line . Write the observation.
- Produce AB to form a ray AE such that exterior angle CBE is formed.
- Make a replica of angle ADC and place it on angle CBE . Write the observation.

**Developmental Questions (What discussion questions)**

- How do you take radius ?
- What is the circumference ?
- What is a chord ?
- What is a quadrilateral ?
- Where are all four vertices of a quadrilateral located ?
- What part are we trying to cut and compare ?
- What can you infer ?

**Evaluation Questions**

- Angle BAD and angle BCD, when placed adjacent to each other on a straight line, completely cover the straight angle.What does this mean ?
- Angle ABC and angle ADC, when placed adjacent to each other on a straight line, completely cover the straight angle.What can you conclude ?
- Compare angle ADC with angle CBE.
- Name the two properties of cyclic quarilaterals.