Difference between revisions of "Theorems on cyclic quadrilaterals"

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m (Preeta moved page Cyclic quadrilaterals to Theorems on cyclic quadrilaterals without leaving a redirect)
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===Name of the activity===
 
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Brief blurb describing what the activity.  If this has been borrowed from some external web site (for example, a non OER or OER site which had this idea and based on which the activity was developed)
 
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=== Objectives ===
 
=== Objectives ===
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Content objectives  - what content areas
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#Both pairs of opposite angles of a cyclic quadrilateral are supplementary.
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#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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Skill objectives - what specific skills
 
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Classroom objectives - to demo peer learning, to make a classroom resource, etc -
 
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All these kinds of objectives need not be there for every activity. And no need to list them as different headings.  This is only for our reference when we are developing activities.
 
  
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Converse theorems:
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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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#If the exterior angle of a quadrilateral is equal to the interior opposite angle, then the quadrilateral is cyclic.
 
===Estimated Time===
 
===Estimated Time===
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40 minutes
  
 
=== Prerequisites/Instructions, prior preparations, if any ===
 
=== Prerequisites/Instructions, prior preparations, if any ===
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Laptop, geogebra file, projector and a pointer
  
 
===Materials/ Resources needed===
 
===Materials/ Resources needed===
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#A cyclic quadrilateral and its properties.
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#The linear pair and exterior angle theorem.
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#The circle theorem (Angle at centre = double the angle at the circumference)
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This geogebra file was done by ITfC-Edu-Team.
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===Process (How to do the activity)===
 
===Process (How to do the activity)===
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How to do the different steps of the activity?
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*Process:
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#The teacher can project the geogebra file and prove the theorems.
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What kinds of questions you can ask for that activity
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*Developmental Questions:
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#How many angles does a cyclic quadrilateral have ?
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What are the student follow-up activities/ questions you can give?
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#Name the opposite angles of it.
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#Name the minor arc.
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Categories:  (Subject) (Topic) (Sub-concept/topic) (Class 6) (Resource format)
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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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Example -  (Mathematics) (Triangle) (Area) (Perimeter) (Class 6) (Class 8) (Geogebra) (Video)
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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

Revision as of 07:05, 8 May 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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