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.