Difference between revisions of "Quadrilaterals"

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== '''Concept Map''' ==
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<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;">
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<mm>[[Quadrilaterals.mm|flash]]</mm>
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''[http://karnatakaeducation.org.in/KOER/index.php/ಬಹು_ಭುಜಾಕೃತಿಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div>
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| style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
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| 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]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
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| style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |
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[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
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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 ===
 +
{{#drawio:mmQuadrilaterals1}}
 +
 
 +
==Textbook==
 +
To add textbook links, please follow these instructions to: ([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
 +
==Additional Information==
 +
This videos is related to classification and properties of quadrilaterals.
 +
 
 +
{{#widget:YouTube|id=0OW2bU0So-4}}    {{#widget:YouTube|id=udS3nkj2cfg}}
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===Useful websites===
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#[http://www.shodor.org/ihnteractivate/discussions/Quadrilaterals/ click here] : For effective introduction to quadrilaterals.
 +
#[http://www.mathopenref.com/quadrilateral.html click here]  : Simple explanation about quadrilaterals.
 +
#[http://www.slideshare.net/muzzu1999/types-of-quadrilaterals-and-its-properties-group-4 click here]  : This website has a very good activity on properties of quadrilaterals.
 +
#[http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i1/bk8_1i3.htm click here]  This is a very good website for students to understand classification of quadrilaterals as per their properties.
 +
===Reference Books===
 +
*Please download 9th standard mathematics textbook of Tamil Nadu state syllabus from the following link and refer the page 89 [http://www.textbooksonline.tn.nic.in/Std9.htm click here]
 +
*Refer 9th standard mathematics ncert  textbook from the following link [http://www.ncert.nic.in/ncerts/textbook/textbook.htm?iemh1=8-15 click here]
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=== Additional Resources  ===
 +
 
 +
==== Resource Title ====
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[http://www.mathopenref.com/tocs/quadrilateraltoc.html Quadrilaterals]
  
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= Text Books =
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==== OER  ====
 +
# List web resources with a  brief description of what it contains; how it can be used and whether it can be by teacher/ student or both
 +
# Books and journals
 +
# Textbooks
 +
# Syllabus documents
  
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Please refer the state govt. Text book of mathematics
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==== Non-OER  ====
 +
# List web resources with a  brief description of what it contains; how it can be used and whether it can be by teacher/ student or both
 +
#* http://www.mathopenref.com/quadrilateral.html : Simple explanation about quadrilaterals.
 +
#* http://www.slideshare.net/muzzu1999/types-of-quadrilaterals-and-its-properties-group-4  : This website has a very good activity on properties of quadrilaterals.
 +
#* http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i1/bk8_1i3.htm    This is a very good website for students to understand classification of quadrilaterals as per their properties.
 +
#* http://www.shodor.org/ihnteractivate/discussions/Quadrilaterals/ click here : For effective introduction to quadrilaterals.
 +
# Books and journals
 +
#* Please download 9th standard mathematics textbook of Tamil Nadu state syllabus from the following link and refer to page 89 [http://www.textbooksonline.tn.nic.in/Std9.htm click here]
 +
#* Refer 9th standard mathematics NCERT textbook from the following link [http://www.ncert.nic.in/ncerts/textbook/textbook.htm?iemh1=8-15 click here]
 +
# Textbooks : Karnataka State Text book of mathematics [http://ktbs.kar.nic.in/new/website%20textbooks/class9/9th%20standard/9th-english-maths-1.pdf Class 9-Chapter 8:Quadrilaterals]
 +
# Syllabus documents (CBSE, ICSE, IGCSE etc)
  
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=Additional Information=
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= Additional Information =
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==Useful websites==
+
An Ortho-diagonal quadrilateral i.e., any quadrilateral whose diagonals are perpendicular to each other possesses certain interesting properties. This article [http://azimpremjiuniversity.edu.in/SitePages/pdf/quadrilaterals-with-perpendicular-diagonals.pdf 'Quadrilaterals with Perpendicular Diagonals'] by Shailesh Shirali (published in ''<nowiki/>'At Right Angles''' | Vol. 6, No. 2, August 2017) discusses a few of them.  
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* Effective Introduction to Quadrilateral [http://www.shodor.org/ihnteractivate/discussions/Quadrilaterals/ click here]<br>
 
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* Quadrilateral is also tetragon, quadrangle [http://www.mathopenref.com/quadrilateral.html click here]
 
  
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==Reference Books==
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''<nowiki/>''
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* Please download 9th standard mathematics textbook of Tamil Nadu state syllabus from the following link and refer the page 89 [http://www.textbooksonline.tn.nic.in/Std9.htm click here]
 
−
* Refer 9th standard mathematics ncert  textbook from the following link [http://www.ncert.nic.in/ncerts/textbook/textbook.htm?iemh1=8-15 click here]
 
  
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= Teaching Outlines =
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=== Learning Objectives ===
 
*  Introduction to polygons  
 
*  Introduction to polygons  
 
*  The meaning of quadrilateral
 
*  The meaning of quadrilateral
Line 24: Line 76:
 
* Introduction to cyclic quadrilaterals
 
* Introduction to cyclic quadrilaterals
  
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==Concept #Introduction to Quadrilaterals==
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=== Teaching Outlines ===
 +
====Concept 1: Introduction to Quadrilaterals====
 +
The word quadrilateral comes from two latin words "quadri" which means a "variant of 4" and 'latera' which means 'side'. A quadrilateral is a 4 sided figure with 4 sides, 4 angles and 4 vertices.
 +
 
 +
This topic has its basics in polygons. Try to elicit live examples for quadrilaterals from within classroom, starting from the shape of a textbook. Show the vertices of a rectangular page.  Mark three sets of four  points on the blackboard, one set being collinear and other non-collinear. Call students to join the points of each set of points. This activity will introduce them to the concept of quadrilateral.
 +
 
 +
===== Activities # =====
 +
 
 +
====== [[Introduction to quadrilaterals]] ======
 +
This activity explores formation of a quadrilateral and elements related with the shape.
 +
 
 +
======[[Identifying quadrilaterals]]======
 +
This is an exploration into quadrilaterals. A specific type of quadrilateral can be selected with the checkboxes, and any blue dots on each quadrilateral can be dragged to change the shape.
 +
 
 +
====== Concept 3: Types of quadrilaterals ======
 +
Quadrilaterals are of different types. Grouping is made based on the four angle measures and/or sides. Each type is recognized with its characteristic properties. The types include regular, non-regular; convex, concave; parallelogram (square, rectangle, rhombus,) and non-parallelograms (trapezium and kite).
 +
 
 +
===== Activities # =====
 +
 
 +
====== [[Quadrilaterals "I have - Who has?"|"I have - Who has ?"]]======
 +
A hands on group activity that helps in identifying and building vocabulary related to quadrilaterals.
 +
 
 +
====== [[Venn diagrams of quadrilaterals]] ======
 +
Classifying quadrilaterals based on their properties and identifying related quadrilaterals with ven-diagram.
 +
 
 +
==== Concept 2: Properties of quadrilaterals ====
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There are certain characteristic properties by which a quadrilateral is identified. A quadrilateral is a plane closed figure having 4 sides and 4 angles. The sum of all 4 interior angles of any quadrilateral always equals to 360 degrees. This is called the interior angle sum property of a quadrilateral. The sum of all 4 exterior angles of any quadrilateral equals 360 degrees. This is called the exterior angle sum property of the quadrilateral. If any 3 angles of a quadrilateral are known the fourth angle can be found using the angle sum property.
 +
 
 +
===== Activities # =====
 +
 
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====== [[Angle sum property of a quadrilateral]]======
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Showing the sum of angles of quadrilaterals by placing the angles of the quadrilateral adjacent to each other with a hand on activity.
 +
 
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====== [[Sum of the interior angles of a quadrilateral]] ======
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The sum of the measures of the angles in any quadrilateral is 4 right angles.
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 +
====== [[Sum of angles at point of intersection of diagonals in a quadrilateral]] ======
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A diagonal is the line segment that joins a vertex of a polygon to any of its non-adjacent vertices. These two diagonals of a quadrilateral form angle, this activity explores the property of these angles.
 +
 
 +
====== [[Area of a quadrilateral]] ======
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A diagonal divides a quadrilateral into 2 triangles. Understanding the area of a quadrilateral in terms of triangles is done with this activity.
 +
 
 +
==== [[Properties of Parallelogram]] ====
 +
 
 +
==== [[Parallelogram on same base and between same parallels have equal area]] ====
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 +
==== [[Mid point of sides of a Quadrilateral forms parallelogram]] ====
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 +
==== Concept 3 : Properties of Rhombus ====
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A rhombus is a quadrilateral with all sides of equal length. The opposite angles of a rhombus are equal and its diagonals are perpendicular bisectors of one another. Since the opposite sides and opposite angles of a rhombus have the same measures, it is also a parallelogram. Hence, a rhombus has all properties of a parallelogram and also that of a kite. [[Properties of Rhombus|(click here)]]
 +
 
 +
==== Concept 3: Construction of quadrilaterals ====
  
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===Learning objectives===
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==== Concept 4: Square ====
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* Students will be able to  define quadrilaterals.
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A square is a 4-sided regular polygon with all sides equal and all internal angles 90. A square is the only regular quadrilateral. It can also be considered as a special rectangle with both adjacent sides equal. Its opposite sides are parallel. The diagonals are congruent and bisect each other at right angles. The diagonals bisect the opposite angles. Each diagonal divides the square into two congruent isosceles right angled triangles. A square can be inscribed in a circle. A circle can be inscribed in a square touching all its sides.
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* Students will be able to identify quadrilaterals.
 
  
−
===Notes for teachers===
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[[Introduction to a square and its properties|Click here : Introduction to a square and its properties]]
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This topic has its basics in polygons. Try to elicit live examples for quadrilaterals from within classroom, starting from the shape of a textbook. Show the vertices of a rectangular page.  Mark three sets of four  points on the blackboard, one set being collinear and other non-collinear. Call students to join the points of each set of points. This activity will introduce them to the concept of quadrilateral.
 
  
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===Activity No # Identifying quadrilaterals.===
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Four sides of a square are equal. Adjacent sides are at right angles with each other. The area of a square is side x side sq units. The perimeter of a square is the length of distance around its boundary which is 4 times its side.
−
*Materials/ Resources needed
 
−
Pattern blocks for per students, blank paper, colored pencils
 
−
*Estimated time
 
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10-15 minutes
 
−
*Prerequisites/Instructions, if any
 
−
Student should be able to recognize polygons having different sides especialy four.
 
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*Multimedia resources
 
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Computer, projector
 
−
*Website interactives/ links/ / Geogebra Applets
 
−
Geogebra activities on Quadrilateral [http://www.geogebratube.org/material/show/id/3785 click here]
 
−
*Process/ Developmental Questions
 
−
1. Set the stage by playing a short game of “If you are…” with the students. When students    match what you are saying they stand up. When they sit back down, call out another “If you  are _______ stand up now” statement. To end the game, tell the students to turn to a  neighbor and tell them all of the different names that applied to them.<br> 
 
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2. Review the vocabulary words: sides and angles.<br>
 
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3. Tell students to take one of each of the type of pattern blocks out of the bag.<br>
 
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4. Ask students to sort their pattern blocks – do not tell them how to sort.<br>
 
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5. Go around and have each student tell you how they sorted.  Write the different ways on the board.  For duplicates, begin making tallies.
 
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6. Refer to the list (some students should have mentioned that they sorted by the number of sides).  Point out the number of sides/angles as the sorting rule.<br>
 
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7. Tell students that all of the blocks with four sides and four angles belong to the same family.  That family is the “Quadrilateral” family.  Explain that the blocks can have many names – just like you can be called many names.<br>
 
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8. Have the students to fold their paper in half and to draw a line down the middle of the paper.  On one half of the paper, write the word “Quadrilaterals”. On the other half of the paper write the words “Not Quadrilaterals.”  Prior to teaching create an example for students to go by.<br>
 
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9. Have students trace each different pattern block on the correct side of the paper.<br> 
 
−
10.When all of the students have traced the pattern blocks on their papers, have different students come up to overhead/document camera.  The student should place a pattern block on the correct half of the paper so that students can all check their work.
 
−
*Evaluation
 
−
1. What do all of your quadrilaterals have in common?<br>
 
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2. What is different about the quadrilaterals?<br>
 
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3. What did you put the hexagon on this half of the page?Please study the state govt. Text book of mathematics.<br>
 
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4. Can you combine your blocks to make different quadrilaterals?
 
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*Question Corner
 
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List out the quadrilaterals in this home.
 
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[[File:eee.png]]
 
  
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==Concept # 2.Properties of quadrilaterals==
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====== [[Pull me to see if I still remain a square]] ======
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===Learning objectives===
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===Notes for teachers===
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====== [[Area of a square]] ======
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===Activity No # ===
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[[Constructing a square|'''Constructing a square''']]
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{| style="height:10px; float:right; align:center;"
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|<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;">
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==== Concept 5: Cyclic Quadrilaterals ====
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''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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|}
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==== [[Cyclic Quadrilaterals]] ====
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*Estimated Time
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*Materials/ Resources needed
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====== [[Theorems on cyclic quadrilaterals]] ======
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*Prerequisites/Instructions, if any
+
 
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*Multimedia resources
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==== Concept : Kite ====
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*Website interactives/ links/ / Geogebra Applets
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A kite has two pairs of congruent sides. Its diagonals intersect at right angles. The sum of its four sides would be its perimeter. Its area is given by the formula <math>(1/2) (product  of  its  diagnols)</math>
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*Process/ Developmental Questions
+
 
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*Evaluation
+
====== [[A Kite and its properties]] ======
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*Question Corner
+
 
 +
====== [[Construction of a kite]] ======
 +
 
 +
====== [[Deriving formula for area of a kite]] ======
 +
 
 +
==== Concept : Trapezium ====
 +
 
 +
======[[A Trapezium and its properties]]======
  
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==Concept #3. Types of quadrilaterals==
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====== [[Deriving formula for area of a trapezium]] ======
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===Learning objectives===
 
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===Notes for teachers===
 
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===Activity No # Tangram===
 
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This activity has been taken from the website :http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bs7act1.pdf
 
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{| style="height:10px; float:right; align:center;"
 
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|<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;">
 
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''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
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|}
 
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[[File:Tangram.jpg|200px]]
 
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*Estimated Time : 40 minutes.
 
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*Materials/ Resources needed: Chart papers, scissors, pencil, scale.
 
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*Prerequisites/Instructions, if any
 
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# The students should have understanding of basic shapes like square, rectangle, parallelogram, triangle and trapezium.
 
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# They should be able to draw mentioned shapes accurately and cut exactly on boundaries.
 
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*Multimedia resources
 
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*Website interactives/ links/ / Geogebra Applets
 
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*Process:
 
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# This is a very old Chinese puzzle known as a tangram.
 
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# Cut out the square below into 7 shapes.
 
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# Cut out the 7 shapes and rearrange them to form:
 
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(a) a square from two triangles, and then change it to a parallelogram;
 
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(b) a rectangle using three pieces, and then change it into a parallelogram;
 
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(c) a trapezium with three pieces;
 
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(d) a parallelogram with four pieces;
 
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(e) a trapezium from the square, parallelogram and the two small triangles;
 
−
(f) a triangle with three pieces;
 
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(g) a rectangle with all seven pieces.
 
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# Finally, put the pieces back together to form the original square.
 
−
*Developmental Questions:
 
−
# Were you all able to read and follow the instructions.
 
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# Name and point the different shapes in the figure.
 
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# Name the dimensions of each shape.
 
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*Evaluation:
 
−
# Analyse how much space each shape is occupying.
 
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# What can you refer to the space occupied by each shape.
 
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*Question Corner:
 
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# What are the characteristic properties of each shape: square, rectangle, triangle, parallelogram and trapezium ?
 
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# What type of two triangles would you need to form a square ?
 
−
# What did you learn from this activity ?
 
  
 +
====== [[Construction of Trapezium]] ======
  
 +
====== [[Construct an isosceles trapezium and study its properties]] ======
 +
A trapezium in which non-parallel sides are equal is called as an Isosceles Trapezium. The diagonals of an isosceles trapezium are equal. An isosceles trapezium has one line of reflection symmetry. This line connects the midpoints of the two bases. Both pairs of base angles of an isosceles trapezium are congruent. Pairs of angles in an isosceles trapezium that do not share a base are supplementary. The area of an isosceles trapezium is given by<math>(a+b)/2  x  h</math> , where a and b are the lengths of the parallel sides and h is the distance (height) between the parallel sides.
  
 +
===== Solved problems/ key questions (earlier was hints for problems).[edit | edit source] =====
  
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===Activity No # ===
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=== Projects (can include math lab/ science lab/ language lab)[edit | edit source] ===
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{| style="height:10px; float:right; align:center;"
 
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|<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;">
 
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''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
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|}
 
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*Estimated Time
 
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*Materials/ Resources needed
 
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*Prerequisites/Instructions, if any
 
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*Multimedia resources
 
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*Website interactives/ links/ / Geogebra Applets
 
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*Process/ Developmental Questions
 
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*Evaluation
 
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*Question Corner
 
  
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= Fun Corner =
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=== Assessments - question banks, formative assessment activities and summative assessment activities[edit | edit source] ===
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* Math is fun [[http://www.mathsisfun.com/quadrilaterals.html]]
+
[[Category:Class 9]]
 +
[[Category:Quadrilaterals]]

Latest revision as of 08:43, 5 July 2022

ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

The Story of Mathematics

Philosophy of Mathematics

Teaching of Mathematics

Curriculum and Syllabus

Topics in School Mathematics

Textbooks

Question Bank

While creating a resource page, please click here for a resource creation checklist.


Concept Map

Textbook

To add textbook links, please follow these instructions to: (Click to create the subpage)

Additional Information

This videos is related to classification and properties of quadrilaterals.

Useful websites

  1. click here : For effective introduction to quadrilaterals.
  2. click here : Simple explanation about quadrilaterals.
  3. click here : This website has a very good activity on properties of quadrilaterals.
  4. click here This is a very good website for students to understand classification of quadrilaterals as per their properties.

Reference Books

  • Please download 9th standard mathematics textbook of Tamil Nadu state syllabus from the following link and refer the page 89 click here
  • Refer 9th standard mathematics ncert textbook from the following link click here

Additional Resources

Resource Title

Quadrilaterals

OER

  1. List web resources with a  brief description of what it contains; how it can be used and whether it can be by teacher/ student or both
  2. Books and journals
  3. Textbooks
  4. Syllabus documents

Non-OER

  1. List web resources with a  brief description of what it contains; how it can be used and whether it can be by teacher/ student or both
  2. Books and journals
    • Please download 9th standard mathematics textbook of Tamil Nadu state syllabus from the following link and refer to page 89 click here
    • Refer 9th standard mathematics NCERT textbook from the following link click here
  3. Textbooks : Karnataka State Text book of mathematics Class 9-Chapter 8:Quadrilaterals
  4. Syllabus documents (CBSE, ICSE, IGCSE etc)

Additional Information

An Ortho-diagonal quadrilateral i.e., any quadrilateral whose diagonals are perpendicular to each other possesses certain interesting properties. This article 'Quadrilaterals with Perpendicular Diagonals' by Shailesh Shirali (published in 'At Right Angles' | Vol. 6, No. 2, August 2017) discusses a few of them.

Learning Objectives

  • Introduction to polygons
  • The meaning of quadrilateral
  • Identification of various types of quadrilaterals
  • Different properties of special quadrilaterals
  • Construction of quadrilaterals to given suitable data
  • Finding area of quadrilaterals
  • Introduction to cyclic quadrilaterals

Teaching Outlines

Concept 1: Introduction to Quadrilaterals

The word quadrilateral comes from two latin words "quadri" which means a "variant of 4" and 'latera' which means 'side'. A quadrilateral is a 4 sided figure with 4 sides, 4 angles and 4 vertices.

This topic has its basics in polygons. Try to elicit live examples for quadrilaterals from within classroom, starting from the shape of a textbook. Show the vertices of a rectangular page.  Mark three sets of four  points on the blackboard, one set being collinear and other non-collinear. Call students to join the points of each set of points. This activity will introduce them to the concept of quadrilateral.

Activities #
Introduction to quadrilaterals

This activity explores formation of a quadrilateral and elements related with the shape.

Identifying quadrilaterals

This is an exploration into quadrilaterals. A specific type of quadrilateral can be selected with the checkboxes, and any blue dots on each quadrilateral can be dragged to change the shape.

Concept 3: Types of quadrilaterals

Quadrilaterals are of different types. Grouping is made based on the four angle measures and/or sides. Each type is recognized with its characteristic properties. The types include regular, non-regular; convex, concave; parallelogram (square, rectangle, rhombus,) and non-parallelograms (trapezium and kite).

Activities #
"I have - Who has ?"

A hands on group activity that helps in identifying and building vocabulary related to quadrilaterals.

Venn diagrams of quadrilaterals

Classifying quadrilaterals based on their properties and identifying related quadrilaterals with ven-diagram.

Concept 2: Properties of quadrilaterals

There are certain characteristic properties by which a quadrilateral is identified. A quadrilateral is a plane closed figure having 4 sides and 4 angles. The sum of all 4 interior angles of any quadrilateral always equals to 360 degrees. This is called the interior angle sum property of a quadrilateral. The sum of all 4 exterior angles of any quadrilateral equals 360 degrees. This is called the exterior angle sum property of the quadrilateral. If any 3 angles of a quadrilateral are known the fourth angle can be found using the angle sum property.

Activities #
Angle sum property of a quadrilateral

Showing the sum of angles of quadrilaterals by placing the angles of the quadrilateral adjacent to each other with a hand on activity.

Sum of the interior angles of a quadrilateral

The sum of the measures of the angles in any quadrilateral is 4 right angles.

Sum of angles at point of intersection of diagonals in a quadrilateral

A diagonal is the line segment that joins a vertex of a polygon to any of its non-adjacent vertices. These two diagonals of a quadrilateral form angle, this activity explores the property of these angles.

Area of a quadrilateral

A diagonal divides a quadrilateral into 2 triangles. Understanding the area of a quadrilateral in terms of triangles is done with this activity.

Properties of Parallelogram

Parallelogram on same base and between same parallels have equal area

Mid point of sides of a Quadrilateral forms parallelogram

Concept 3 : Properties of Rhombus

A rhombus is a quadrilateral with all sides of equal length. The opposite angles of a rhombus are equal and its diagonals are perpendicular bisectors of one another. Since the opposite sides and opposite angles of a rhombus have the same measures, it is also a parallelogram. Hence, a rhombus has all properties of a parallelogram and also that of a kite. (click here)

Concept 3: Construction of quadrilaterals

Concept 4: Square

A square is a 4-sided regular polygon with all sides equal and all internal angles 90. A square is the only regular quadrilateral. It can also be considered as a special rectangle with both adjacent sides equal. Its opposite sides are parallel. The diagonals are congruent and bisect each other at right angles. The diagonals bisect the opposite angles. Each diagonal divides the square into two congruent isosceles right angled triangles. A square can be inscribed in a circle. A circle can be inscribed in a square touching all its sides.

Click here : Introduction to a square and its properties

Four sides of a square are equal. Adjacent sides are at right angles with each other. The area of a square is side x side sq units. The perimeter of a square is the length of distance around its boundary which is 4 times its side.

Pull me to see if I still remain a square
Area of a square

Constructing a square

Concept 5: Cyclic Quadrilaterals

Cyclic Quadrilaterals

Theorems on cyclic quadrilaterals

Concept : Kite

A kite has two pairs of congruent sides. Its diagonals intersect at right angles. The sum of its four sides would be its perimeter. Its area is given by the formula

A Kite and its properties
Construction of a kite
Deriving formula for area of a kite

Concept : Trapezium

A Trapezium and its properties
Deriving formula for area of a trapezium
Construction of Trapezium
Construct an isosceles trapezium and study its properties

A trapezium in which non-parallel sides are equal is called as an Isosceles Trapezium. The diagonals of an isosceles trapezium are equal. An isosceles trapezium has one line of reflection symmetry. This line connects the midpoints of the two bases. Both pairs of base angles of an isosceles trapezium are congruent. Pairs of angles in an isosceles trapezium that do not share a base are supplementary. The area of an isosceles trapezium is given by , where a and b are the lengths of the parallel sides and h is the distance (height) between the parallel sides.

Solved problems/ key questions (earlier was hints for problems).[edit | edit source]

Projects (can include math lab/ science lab/ language lab)[edit | edit source]

Assessments - question banks, formative assessment activities and summative assessment activities[edit | edit source]

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