Difference between revisions of "Theorems on cyclic quadrilaterals"

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__FORCETOC__
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=== Objectives ===
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=Activity - Cyclic Quadrilateral=
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#Both pairs of opposite angles of a cyclic quadrilateral are supplementary.
 +
#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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==Estimated Time==
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Converse theorems:
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10 minutes
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#Suppose a quadrilateral is such that the sum of two opposite angles is a straight angle, them the quadrilateral is cyclic.
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==Materials/ Resources needed==
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#If the exterior angle of a quadrilateral is equal to the interior opposite angle, then the quadrilateral is cyclic.
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Laptop, geogebra file, projector and a pointer.
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===Estimated Time===
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==Prerequisites/Instructions, if any==
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40 minutes
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# Circles and quadrilaterals should have been covered.
 
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==Multimedia resources==
 
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Laptop
 
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==Website interactives/ links/ simulations/ Geogebra Applets==
 
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This geogebra file was created by ITfC-Edu-Team.
 
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<ggb_applet width="1282" height="601" version="4.0" ggbBase64="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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
 
  
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==Process (How to do the activity)==
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=== Prerequisites/Instructions, prior preparations, if any ===
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# Show the geogebra file.
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Laptop, geogebra file, projector and a pointer
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# Move points, the vertices of the quadrilateral and let the students observe the sum of opposite interior angles.
 
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==Developmental Questions (What discussion questions)==
 
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# What two figures do you see in the figure ?
 
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# Name the vertices of the quadrilateral.
 
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# Where are all the 4 vertices situated ?
 
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# Name the opposite interior angles of the quadrilateral.
 
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# What do you observe about them.
 
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==Evaluation (Questions for assessment of the child)==
 
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# Compare the cyclic quadrilateral to circumcircle.
 
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==Question Corner==
 
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# Name this special quadrilateral.
 
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==Activity Keywords==
 
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#Geogebra
 
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#Cyclic Quadrilateral
 
  
 +
===Materials/ Resources needed===
 +
#A cyclic quadrilateral and its properties.
 +
#The linear pair and exterior angle theorem.
 +
#The circle theorem (Angle at centre = double the angle at the circumference)
 +
This geogebra file was done by ITfC-Edu-Team.
  
 +
===Process (How to do the activity)===
 +
*Process:
 +
#The teacher can project the geogebra file and prove the theorems.
 +
*Developmental Questions:
 +
#How many angles does a cyclic quadrilateral have ?
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#Name the opposite angles of it.
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#Name the minor arc.
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#Recall the angle -arc theorem.
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#What is the total angle at the centre of a circle ?
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#Name the angles at the centre of the circle.
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#What is the sum of those two angles ?
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#How can you show that
  
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'''To link back to the concept page'''
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[[Category:Quadrilaterals]]
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<nowiki>
 
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[http://karnatakaeducation.org.in/KOER/en/index.php/'''Give the link of the page name from where activity was given''' Back]
 

Latest revision as of 09:45, 11 November 2019

Objectives

  1. Both pairs of opposite angles of a cyclic quadrilateral are supplementary.
  2. When one side of a cyclic quadrilateral is produced, the exterior angle so formed is equal to the interior opposite angle.

Converse theorems:

  1. Suppose a quadrilateral is such that the sum of two opposite angles is a straight angle, them the quadrilateral is cyclic.
  2. If the exterior angle of a quadrilateral is equal to the interior opposite angle, then the quadrilateral is cyclic.

Estimated Time

40 minutes

Prerequisites/Instructions, prior preparations, if any

Laptop, geogebra file, projector and a pointer

Materials/ Resources needed

  1. A cyclic quadrilateral and its properties.
  2. The linear pair and exterior angle theorem.
  3. The circle theorem (Angle at centre = double the angle at the circumference)

This geogebra file was done by ITfC-Edu-Team.

Process (How to do the activity)

  • Process:
  1. The teacher can project the geogebra file and prove the theorems.
  • Developmental Questions:
  1. How many angles does a cyclic quadrilateral have ?
  2. Name the opposite angles of it.
  3. Name the minor arc.
  4. Recall the angle -arc theorem.
  5. What is the total angle at the centre of a circle ?
  6. Name the angles at the centre of the circle.
  7. What is the sum of those two angles ?
  8. How can you show that
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