Difference between revisions of "Cyclic quadrilateral"

From Karnataka Open Educational Resources
Jump to navigation Jump to search
m (Text replacement - "<mm>[[" to "[[File:")
m (added Category:Circles using HotCat)
 
(5 intermediate revisions by 2 users not shown)
Line 1: Line 1:
 +
A quadrilateral ABCD is called cyclic if all four vertices of it lie on a circle.In a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.If the sum of a pair of opposite angles of a quadrilateral is 180, the quadrilateral is cyclic.In a cyclic quadrilateral the exterior angle is equal to interior opposite angle.
  
<!-- This portal was created using subst:box portal skeleton  -->
+
===Objectives===
<!--        BANNER ACROSS TOP OF PAGE        -->
+
Understanding cyclic quadrilaterals
{| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;"
 
|-
 
|style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
[http://karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
 
|}
 
While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
 
  
= Concept Map =
+
Relation between angles of a cyclic quadrilateral.
__FORCETOC__
 
[[File:Cyclic_quadrilateral.mm|flash]]</mm>
 
  
= Textbook =
+
===Estimated Time===
To add textbook links, please follow these instructions to:
+
10 minutes
([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
 
  
=Additional Information=
+
===Prerequisites/Instructions, prior preparations, if any===
==Useful websites==
+
Circle and quadrilaterals should have been introduced.
==Reference Books==
 
  
= Teaching Outlines =
+
===Materials/ Resources needed===
 +
Digital : Laptop, geogebra file, projector and a pointer.
  
==Concept # 1. Cyclic quadrilateral and its properties==
+
Geogebra file: [https://ggbm.at/jdxxnrmb Cyclic quadrilateral.ggb]
===Learning objectives===
+
 
# A quadrilateral ABCD is called cyclic if all of its four vertices lie on a circle.
+
{{Geogebra|jdxxnrmb}}
# In a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.
+
 
# If the sum of a pair of opposite angles of a quadrilateral is 180, the quadrilateral is cyclic.
+
===Process (How to do the activity)===
# In a cyclic quadrilateral the exterior angle is equal to interior opposite angle.
+
<span></span><span></span>
===Notes for teachers===
 
===Activity#1 Cyclic quadrilateral ===                                                                                                             
 
*Estimated Time 10 minutes
 
*Materials/ Resources needed: Laptop, geogebra file, projector and a pointer.
 
*Prerequisites/Instructions, if any
 
# Circle and quadrilaterals should have been introduced.
 
*Multimedia resources : Laptop
 
*Website interactives/ links/ / Geogebra Applets
 
<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" />
 
*Process:
 
 
# The teacher can recall the concept of a circle, quadrilateral, circumcircle.
 
# The teacher can recall the concept of a circle, quadrilateral, circumcircle.
 
# Can explain a cyclic quadrilateral and show the geogebra applet.
 
# Can explain a cyclic quadrilateral and show the geogebra applet.
 
# Move points, the vertices of the quadrilateral and let the students observe the sum of opposite interior angles.
 
# Move points, the vertices of the quadrilateral and let the students observe the sum of opposite interior angles.
Developmental Questions:
+
* Developmental Questions:
 
# What two figures do you see in the figure ?
 
# What two figures do you see in the figure ?
 
# Name the vertices of the quadrilateral.
 
# Name the vertices of the quadrilateral.
Line 63: Line 34:
 
*Question Corner  
 
*Question Corner  
 
# Can all quadrilaterals be cyclic ?
 
# Can all quadrilaterals be cyclic ?
# What are the necessary conditions for a quadrilateral to be cyclic ?
+
# What are the necessary conditions for a quadrilateral to be cyclic ?   <span></span><span></span>
 
 
===Activity No # 2.Properties of a Cyclic quadrilateral===                                                                                                         
 
*Estimated Time: 45 minutes
 
*Materials/ Resources needed
 
coloured paper, pair of scissors, sketch pen, carbon paper, geometry box
 
*Prerequisites/Instructions, if any
 
# In a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.
 
# In a cyclic quadrilateral the exterior angle is equal to interior opposite angle
 
*Multimedia resources
 
*Website interactives/ links/ / Geogebra Applets
 
This activity has been taken from the website http://mykhmsmathclass.blogspot.in/2007/11/class-ix-activity-16.html
 
*Process:
 
[[File:c.q.jpeg|300px]]
 
 
 
# Draw a circle of any radius on a coloured paper and cut it.
 
# Paste the circle cut out on a rectangular sheet of paper.
 
# By paper folding get chords AB, BC, CD and DA in order.
 
# Draw AB, BC, CD & DA. A cyclic quadrilateral ABCD is obtained.
 
# Produce AB to form a ray AE such that exterior angle CBE is formed.
 
# Make a replica of cyclic quadrilateral ABCD using carbon paper.
 
# Cut the replica into 4 parts such that each part contains one angle .
 
# Draw a straight line on a paper.
 
# Place the two opposite angles, angle BAD and angle BCD adjacent to each other on the straight line.Write the observation.
 
# Place other two opposite angles, angle ABC and angle ADC adjacent to each other on the straight line . Write the observation.
 
# Make a replica of angle ADC and place it on angle CBE . Write the observation.
 
Developmental Questions:
 
# How do you take radius ?
 
# What is the circumference ?
 
# What is a chord ?
 
# What is a quadrilateral ?
 
# Where are all four vertices of a quadrilateral located ?
 
# What part are we trying to cut and compare ?
 
# What can you infer ?
 
*Evaluation:
 
# Angle BAD and angle BCD, when placed adjacent to each other on a straight line, completely cover the straight angle.What does this mean ?
 
# Angle ABC and angle ADC, when placed adjacent to each other on a straight line, completely cover the straight angle.What can you conclude ?
 
# Compare angle ADC with angle CBE.
 
*Question Corner:
 
Name the two properties of cyclic quarilaterals.
 
 
 
==Concept # 2.Construction of cyclic quadrilateral==
 
===Learning objectives===
 
# Ability to construct a cyclic quadrilateral accurately .
 
===Notes for teachers===
 
===Activity No # Constructing a cyclic quadrilateral===
 
{| 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;">
 
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
*Estimated Time: 40 minutes.
 
*Materials/ Resources needed:
 
# Laptop, geogebra file, projector and a pointer.
 
# Students constructing materials, the geometry box.
 
# white papers.
 
*Prerequisites/Instructions, if any
 
# Sufficient knowledge regarding construction of perpendicular lines, bisectors, angles and circle.
 
*Multimedia resources : Laptop
 
*Website interactives/ links/ / Geogebra Applets: For step by step illustration of cyclic quadrilateral construction please refer to the website:  http://www.matrusrieppower.net/Constructionoftriangleandcyclicquadrilateral.html. 
 
*Process:
 
# The teacher can do this activity after introducing the concept and properties of cyclic quadrilateral.
 
# She can project the file and let students watch it carefully.
 
# After watching discuss the steps of construction and the purpose of each step so that the students can appreciate the sequence of construction steps.
 
# Then ask the students to actually construct a cyclic quadrilateral for the given measures.
 
*Developmental Questions:
 
# What is a cyclic quadrilateral ? Why is it called so ?
 
# Name the measuring parameters of it ?
 
# What measures are given for its construction ?
 
# Explain the steps involved in determing the radius of the required circle ?
 
# What do the measures of the arcs specify ?
 
*Evaluation:
 
# Were the students able to justify the sequence of steps involved ?
 
*Question Corner:
 
# Can you draw a circle first and then the quadrilateral ? Why not so ?
 
 
 
===Activity No # ===
 
{| 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;">
 
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
*Estimated Time
 
*Materials/ Resources needed
 
*Prerequisites/Instructions, if any
 
*Multimedia resources
 
*Website interactives/ links/ / Geogebra Applets
 
*Process/ Developmental Questions
 
*Evaluation
 
*Question Corner
 
 
 
==Concept # 3. Theorems on cyclic quadrilaterals==
 
===Learning objectives===
 
# 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.<br>
 
Converse theorems:
 
# Suppose a quadrilateral is such that the sum of two opposite angles is a straight angle, them the quadrilateral is cyclic.
 
# If the exterior angle of a quadrilateral is equal to the interior opposite angle, then the quadrilateral is cyclic.
 
===Notes for teachers===
 
===Activity No 1. Theorems ===
 
{| 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;">
 
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
*Estimated Time : 40 minutes.
 
*Materials/ Resources needed:
 
Laptop, geogebra file, projector and a pointer.
 
*Prerequisites/Instructions, if any
 
# 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)
 
*Multimedia resources: Laptop
 
*Website interactives/ links/ / Geogebra Applets:
 
This geogebra file was done by ITfC-Edu-Team.
 
<ggb_applet width="1280" height="600" version="4.0" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
 
*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.
 
# What is the total angle at the centre of a circle ?
 
# Name the angles at the centre of the circle.
 
# What is the sum of those two angles ?
 
# How can you show that <b and <d are supplementary from above observations ?
 
*Evaluation;
 
# What is the converse of this theorem.
 
*Question Corner;
 
# Write down the steps to prove the converse of this theorem.
 
 
 
===Activity No #===
 
{| 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;">
 
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
*Estimated Time
 
*Materials/ Resources needed
 
*Prerequisites/Instructions, if any
 
*Multimedia resources
 
*Website interactives/ links/ / Geogebra Applets
 
*Process/ Developmental Questions
 
*Evaluation
 
*Question Corner
 
 
 
= Hints for difficult problems =
 
 
 
= Project Ideas =
 
 
 
= Math Fun =
 
 
 
'''Usage'''
 
  
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
+
[[Category:Circles]]

Latest revision as of 05:31, 31 October 2019

A quadrilateral ABCD is called cyclic if all four vertices of it lie on a circle.In a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.If the sum of a pair of opposite angles of a quadrilateral is 180, the quadrilateral is cyclic.In a cyclic quadrilateral the exterior angle is equal to interior opposite angle.

Objectives

Understanding cyclic quadrilaterals

Relation between angles of a cyclic quadrilateral.

Estimated Time

10 minutes

Prerequisites/Instructions, prior preparations, if any

Circle and quadrilaterals should have been introduced.

Materials/ Resources needed

Digital : Laptop, geogebra file, projector and a pointer.

Geogebra file: Cyclic quadrilateral.ggb


Download this geogebra file from this link.


Process (How to do the activity)

  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.
  • Developmental Questions:
  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. Can all quadrilaterals be cyclic ?
  2. What are the necessary conditions for a quadrilateral to be cyclic ?