Difference between revisions of "Cyclic quadrilateral"

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)

The teacher can recall the concept of a circle, quadrilateral, circumcircle.
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.

Developmental Questions:

What two figures do you see in the figure ?
Name the vertices of the quadrilateral.
Where are all the 4 vertices situated ?
Name the opposite interior angles of the quadrilateral.
What do you observe about them.

Evaluation:

Compare the cyclic quadrilateral to circumcircle.

Question Corner

Can all quadrilaterals be cyclic ?
What are the necessary conditions for a quadrilateral to be cyclic ?

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+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
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-[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
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-[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
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-= Concept Map =
+Relation between angles of a cyclic quadrilateral.
-__FORCETOC__
-= Textbook =
-To add textbook links, please follow these instructions to:
-([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
-=Additional Information=
+===Estimated Time===
-==Useful websites==
+minutes
-==Reference Books==
-= Teaching Outlines =
+===Prerequisites/Instructions, prior preparations, if any===
+Circle and quadrilaterals should have been introduced.
-==Concept #==
+===Materials/ Resources needed===
-===Learning objectives===
+Digital : Laptop, geogebra file, projector and a pointer.
-===Notes for teachers===
-===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://www.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
-===Activity No # ===
+Geogebra file: [https://ggbm.at/jdxxnrmb Cyclic quadrilateral.ggb]
-{| 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://www.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 #==
+{{Geogebra|jdxxnrmb}}
-===Learning objectives===
-===Notes for teachers===
-===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://www.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
-===Activity No # ===
+===Process (How to do the activity)===
-{| style="height:10px; float:right; align:center;"
+<span></span><span></span>
-|<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;">
+# The teacher can recall the concept of a circle, quadrilateral, circumcircle.
-''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+# 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.
-*Estimated Time
+* Developmental Questions:
-*Materials/ Resources needed
+# What two figures do you see in the figure ?
-*Prerequisites/Instructions, if any
+# Name the vertices of the quadrilateral.
-*Multimedia resources
+# Where are all the 4 vertices situated ?
-*Website interactives/ links/ / Geogebra Applets
+# Name the opposite interior angles of the quadrilateral.
-*Process/ Developmental Questions
+# What do you observe about them.
-*Evaluation
+*Evaluation:
-*Question Corner
+# Compare the cyclic quadrilateral to circumcircle.
+*Question Corner
+# Can all quadrilaterals be cyclic ?
+# What are the necessary conditions for a quadrilateral to be cyclic ?   <span></span><span></span>
-==Concept #==
+[[Category:Circles]]
-===Learning objectives===
-===Notes for teachers===
-===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://www.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
-===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://www.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
-===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://www.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 =
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