Quadrilaterals

 ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

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) * http://www.mathopenref.com/quadrilateral.html : Simple explanation about quadrilaterals.
 * 3) * http://www.slideshare.net/muzzu1999/types-of-quadrilaterals-and-its-properties-group-4 : This website has a very good activity on properties of quadrilaterals.
 * 4) * 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.
 * 5) * http://www.shodor.org/ihnteractivate/discussions/Quadrilaterals/ click here : For effective introduction to quadrilaterals.
 * 6) Books and journals
 * 7) * Please download 9th standard mathematics textbook of Tamil Nadu state syllabus from the following link and refer the page 89 click here
 * 8) * Refer 9th standard mathematics ncert textbook from the following link click here
 * 9) Textbooks : Karnataka State Text book of mathematics Class 9-Chapter 8:Quadrilaterals
 * 10) 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

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.

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 check boxes, 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 recognised with its characteristic properties. The types include regular, non-regular; convex, concave; parallelogram (square, rectangle, rhombus,) and non-parallelograms (trapezium and kite).

"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 interior angle sum property of a quadrilateral. The sum of all 4 exterior angles of any quadrilateral equals 360 degrees. This is called exterior angle sum property of the quadrilteral. The opposite angles of any quadrilateral are supplementary. If any 3 angles of a quadrilateral are known the fourth angle can be found using angle sum property.

Angle sum property of a quadrilateral
Showing the sum of angles of a 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. This two diagonals of a quadrilateral form angle, this activity explores property of these angles.

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