Digital textbook - Polygons

digital  textbook

Submitted by,

Sandra Faria,

B.Ed Mathematics.

POLYGONS

Contents

TOPICS	PAGE
Polygons	4
Types of Polygons	7
Naming polygons	9
Sum of angles of a Polygon	10

Polygons

A polygon is any 2-dimensional shape formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons. The word ‘polygon’ is derived from the greek words ‘poly’ which means ‘many’ and ‘gon’ means ‘angles’.

The name tells you how many sides the shape has. For example, a triangle has three sides, and a quadrilateral has four sides. So any shape that can be drawn by connecting three straight lines is called a triangle, and any shape that can be drawn by connecting four straight lines is called a quadrilateral.

 There are some that wish to name every possible polygon, but there seems a little point in doing so. For example, a 42-sided polygon is called a ‘tetracontakaidigon’.

Beyond about 10 sides, most people call them an ‘n-gon’. For example, a 15-gon has 15 sides. This seems easier to remember and understand.

All of the shapes below are polygons. Notice how all the shapes are drawn with only straight lines? This is what makes a polygon.

If the shape had curves or didn’t fully connect, then it can’t be called a polygon. The orange shape is still a polygon even if it looks like it has an arrow. All the sides are straight, and they are all connected. The orange shape has 11 sides.

Thus, polygons are two dimensional closed shapes and they are made of straight lines.

Now can you answer the following table keeping in mind the properties of a polygon???

Types of Polygons

Now let’s go through some of the common types of polygons. Are you ready for it???

1) Regular or Irregular Polygons

A regular polygon has all angles equal and all sides equal, otherwise it is irregular.

     

2) Concave or Convex Polygons

A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°.
If any internal angle is greater than 180° then the polygon is concave. (Think: concave has a "cave" in it)

3) Simple or Complex Polygons

A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself. Many rules about polygons don't work when it is complex.

Naming of Polygons

Sum of angles of a polygon

We know that the sum of angles of a triangle is ________ .

Do we get the same sum for the angles of a quadrilateral?

How about a pentagon?

Thus, the formula for calculating the sum of the interior angles of a regular polygon is (n - 2) × 180° where n is the number of sides of the polygon.

This formula comes from dividing the polygon up into triangles using full diagonals.

Now can you complete the following table…???

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HEALTH GUIDANCE CLASS

Health guidance class at St. John's H. S, Eravipuram

Innovative lesson plan

INNOVATIVE LESSON TEMPLATE

Name of the teacher trainee: Sandra Faria                                                                 Standard: VIII C

Name of the school: St. John’s H.S, Eravipuram                                                         Strength:

Subject: Mathematics                                                                                                      Duration: 45’

Unit: Polygons                                                                                                                   Date: 17/8/17

Topic: Polygons and Exterior Angles

Curricular Statement: The students will be able to understand the concept of polygons and its exterior angles

                                          through  group activities, discussion and analysis.

Content Analysis          

Term: Polygons

Facts: 1) A two dimensional closed figure with atleast three sides.

            2) The sum of exterior angles of any polygon is 360º.

Concept: Concept of polygons and its exterior angles.

Process: Activities to understand the concept of polygons and its exterior angles.

Learning outcomes: The students will be able to

·        recall related knowledge about polygons.

·        describe the peculiarities of polygons.

·        interpret the concept about polygons and its exterior angles.

·        apply the above concept in a new or unfamiliar situation.

·        judge the appropriateness of the above concept in a given problem.

·        plan new ideas based on the concept.

·        explain the concept of polygons and its exterior angles.

·        develop positive attitude towards Mathematics.

·        accept the beauty of Mathematics and its concepts.

Pre-requisites: Knowledge about polygons, angles around a point and sum of interior angles of a polygon.

Learning aids: Innovative work model, match sticks, string, protractor and blackboard.

CLASSROOM INTERACTION PROCEDURE

PUPIL’S RESPONSE

INTRODUCTION       The teacher starts the class with the following riddle: Iam a two dimensional shape. Iam a closed figure. I have more than two sides I have equal number of edges and vertices. I have no adjacent sides as collinear. Can you tell who I am? Yes. Can you give me examples of polygons? PRESENTATION ACTIVITY The teacher shows the following innovative work model and explains how it was made and its purpose. The teacher now asks each student from a bench to demonstrate any polygon using a string. So you know all about the shapes of a polygon, isn’t it? Now let us learn about exterior angles of a polygon. APPLICATION The teacher distributes matchsticks and ask the students to make a triangle with it. Now can you extend all its sides using the given matchsticks. Can you measure all its outer or exterior angles slowly without shaking the arranged matchsticks? What is the sum of exterior angles of a triangle? The teacher now asks the students to find the sum of exterior angle of a quadrilateral. What is the sum of exterior angles of a quadrilateral? Yes. In the same way find out for pentagon also. What is the sum of exterior angles of a pentagon? REVIEW What did we learn today? So what is a polygon? What is the sum of exterior angles of any polygon?

Polygons Triangle, Quadrilaterals, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon, etc. Triangle Quadrilateral Pentagon Hexagon Yes Yes 360 º It is also 360 º It is also 360 º Polygons and its exterior angles. A polygon is a closed 2- dimensional figure with atleast three sides. 360 º

FOLLOW UP ACTIVITY

·        Draw a picture of your choice using only geometrical shapes.

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Independence Day at St. John's, Eravipuram