Quadrilaterals

ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

Concept Map

[maximize][fold]

Additional Resources

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
   • 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.
2. Books and journals
   • 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
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.

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

Sum of the interior angles of a quadrilateral

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

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).

Venn diagrams of quadrilaterals

Click to Comment