Quadrilaterals

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Concept Map

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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
  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.

Activities #
Identifying quadrilaterals
Introduction to quadrilaterals

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).

Activities #
"I have - Who has ?"
Venn diagrams of quadrilaterals

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.

Activities #
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
Area of a quadrilateral
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