Quadrilaterals

 ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

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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.

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.

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.

Area of a square
Constructing a square

Concept : Kite
A kite has two pairs of congruent sides. Its diagnols intersect at right angles. The sum of its four sides would be its perimetre. Its area is given by the formula $$(1/2) (product  of   its   diagnols)$$

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. Area of isosceles trapezium is given by$$(a+b)/2 x  h$$, where a and b are the lengths of the parallel sides and h is the distance (height) between the parallel sides.