Properties of cyclic quadrilateral

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>

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

• Developmental Questions (What discussion questions)

1. How do you take radius ?
2. What is the circumference ?
3. What is a chord ?
4. What is a quadrilateral ?
5. Where are all four vertices of a quadrilateral located ?
6. What part are we trying to cut and compare ?
7. What can you infer ?

• Evaluation Questions

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