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" 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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.
  
−
[http://karnatakaeducation.org.in/KOER/en/index.php/Circles_and_lines Back]
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===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 ?
 +
#Name the opposite angles of it.
 +
#Name the minor arc.
 +
#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 ?
 +
#How can you show that
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[[Category:Quadrilaterals]]

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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