Cyclic quadrilateral

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Learning objectives

 * 1) A quadrilateral ABCD is called cyclic if all of its four vertices lie on a circle.
 * 2) In a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.
 * 3) If the sum of a pair of opposite angles of a quadrilateral is 180, the quadrilateral is cyclic.
 * 4) In a cyclic quadrilateral the exterior angle is equal to interior opposite angle.

Activity#1 Cyclic quadrilateral
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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" /> Developmental Questions:
 * Estimated Time 10 minutes
 * Materials/ Resources needed: Laptop, geogebra file, projector and a pointer.
 * Prerequisites/Instructions, if any
 * 1) The students should know a circle and its parts.
 * 2) They should know that a quadrilateral is a 4 sided closed figure.
 * Multimedia resources : Laptop
 * Website interactives/ links/ / Geogebra Applets
 * Process:
 * 1) The teacher can recall the concept of a circle, quadrilateral, circumcircle.
 * 2) Can explain a cyclic quadrilateral and show the geogebra applet.
 * 3) Move points, the vertices of the quadrilateral and let the students observe the sum of opposite interior angles.
 * 1) What two figures do you see in the figure ?
 * 2) Name the vertices of the quadrilateral.
 * 3) Where are all the 4 vertices situated ?
 * 4) Name the opposite interior angles of the quadrilateral.
 * 5) What do you observe about them.
 * Evaluation:
 * 1) Compare the cyclic quadrilateral to circumcircle.
 * Question Corner
 * 1) Name this special quadrilateral.

Activity No # 2.Properties of a Cyclic quadrilateral
coloured paper, pair of 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 Note: Refer the above geogebra file to understand the below mentioned labelling. Developmental Questions: Name the two properties of cyclic quarilaterals.
 * Estimated Time: 45 minutes
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * 1) The students should know a circle and a quadrilateral.
 * 2) They should know that in a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.
 * 3) In a cyclic quadrilateral the exterior angle is equal to interior opposite angle
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process:
 * 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.
 * 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:
 * 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.
 * Question Corner:

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
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 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No

 * Estimated Time :
 * Materials/ Resources needed:
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process:
 * Developmental Questions;
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

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