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Line 1: + − <!-- This portal was created using subst:box portal skeleton -->+ − <!-- BANNER ACROSS TOP OF PAGE -->+ − {| 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://www.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://www.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://www.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://www.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://www.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://www.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://www.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 =+ − __FORCETOC__ − <mm>[[Cyclic_quadrilateral.mm|flash]]</mm> − + − To add textbook links, please follow these instructions to: + − ([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage]) − + − + − ==Reference Books== − + + − ==Concept #1. What is a Cyclic quadrilateral ?==+ − ===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 # ===+ − − |<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 − + − ===Learning objectives===+ − ===Notes for teachers===+ − ===Activity No #1.Both pairs of opposite angles of a cyclic quadrilateral are supplementary ===+ − {| 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>+ − |}+ − + − *Materials/ Resources needed+ − + − *Multimedia resources+ − *Website interactives/ links/ / Geogebra Applets+ − *Process/ Developmental Questions+ − *Evaluation+ − *Question Corner+ − ===Activity No # 2. When one side of a cyclic quadrilateral is produced, the exterior angle so formed is equal to the interior opposite angle===+ − {| 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 #3. Suppose a quadrilateral is such that the sum of two opposite angles is a straight angle, then the quadrilateral is a cyclic quadrilteral. === − {| 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 = − − '''Usage''' − − Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
added Category:Circles using HotCat
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.
= Textbook =
===Estimated Time===
10 minutes
=Additional Information=
===Prerequisites/Instructions, prior preparations, if any===
==Useful websites==
Circle and quadrilaterals should have been introduced.
= Teaching Outlines =
===Materials/ Resources needed===
Digital : Laptop, geogebra file, projector and a pointer.
Geogebra file: [https://ggbm.at/jdxxnrmb Cyclic quadrilateral.ggb]
{{Geogebra|jdxxnrmb}}
{| style="height:10px; float:right; align:center;"
==Concept #2. Theorems ==
===Process (How to do the activity)===
<span></span><span></span>
# 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.
*Estimated Time
# Where are all the 4 vertices situated ?
# Name the opposite interior angles of the quadrilateral.
*Prerequisites/Instructions, if any
# 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 ? <span></span><span></span>
[[Category:Circles]]