Difference between revisions of "Cyclic quadrilateral"

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===Learning objectives===
 
===Learning objectives===
 
===Notes for teachers===
 
===Notes for teachers===
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===Activity No #1.By paper folding, cutting and pasting verify that
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===Activity No ===
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1) "The sum of interior opposite angles of cyclic quadrilateral is 180 degrees".
 
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2) "In a cyclic quadrilateral the exterior angle is equal to interior opposite angle". ===
 
 
{| style="height:10px; float:right; align:center;"
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
|}
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*Estimated Time :40 minutes
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*Estimated Time :
 
*Materials/ Resources needed:
 
*Materials/ Resources needed:
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Coloured paper, pair if scissors, sketch pen, carbon paper, geometry box
 
 
*Prerequisites/Instructions, if any
 
*Prerequisites/Instructions, if any
 
*Multimedia resources
 
*Multimedia resources
 
*Website interactives/ links/ / Geogebra Applets
 
*Website interactives/ links/ / Geogebra Applets
 
*Process:  
 
*Process:  
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# Draw a circle of any radius on a coloured paper and cut it.
 
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# Paste the circle cut out on a rectangular sheet of paper.
 
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# By paper folding get chords AB, BC, CD and DA in order.
 
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# Draw AB, BC, CD & DA. A cyclic quadrilateral ABCD is obtained.
 
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# Make a replica of cyclic quadrilateral ABCD using carbon paper.
 
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# Cut the replica into 4 parts such that each part contains one angle .
 
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# Draw a straight line on a paper.
 
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# Place angle BAD and angle BCD adjacent to each other on the straight line.Write the observation.
 
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# Place angle ABC and angle ADC adjacent to each other on the straight line . Write the observation.
 
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# Produce AB to form a ray AE such that exterior angle CBE is formed.
 
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# Make a replica of angle ADC and place it on angle CBE . Write the observation.
 
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Observations :
 
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1) angle BAD and angle BCD , when placed adjacent to each other on a straight line, completely cover the straight angle. This means their sum is 180 degrees.
 
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2) angle ABC and angle ADC , when placed adjacent to each other on a straight line, completely cover the straight angle. This means their sum is 180 degrees.
 
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3) The replica of angle ADC completely covers angle CBE.
 
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RESULT: a)The sum of either pair of opposite angle of a cyclic quadrilateral is 180 degrees.
 
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b)In a cyclic quadrilateral, the exterior angle is equal to interior opposite angle.
 
 
*Developmental Questions;
 
*Developmental Questions;
 
*Evaluation
 
*Evaluation

Revision as of 16:16, 16 December 2013

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Concept #1. What is a Cyclic quadrilateral ?

Learning objectives

Notes for teachers

Activity No #

  • Estimated Time
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  • Process/ Developmental Questions
  • Evaluation
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Activity No #

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  • Prerequisites/Instructions, if any
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  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Concept #2. Theorems

Learning objectives

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Activity No

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Activity No # 2. When one side of a cyclic quadrilateral is produced, the exterior angle so formed is equal to the interior opposite angle

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Activity No #3. Suppose a quadrilateral is such that the sum of two opposite angles is a straight angle, then the quadrilateral is a cyclic quadrilteral.

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