Geogebra/C3/Relationship-between-Geometric-Figures/English

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Title of script: Relationship between Geometric Figures

Author: Madhuri Ganapathi

Keywords: Cyclic quadrilateral, Incircle, Compass, Segment between two points, Circle with center through point, Polygon, Perpendicular bisector, Angle bisector, Angle "Regular Polygon , Move, video tutorial.

Click here for Slides

Visual Cue Narration
Slide Number 1

Hello everybody.

Welcome to the Geogebra tutorial on Relationship between different Geometric Figures in Geogebra

We assume that you have the basic working knowledge of Geogebra.

If not, please go through the “Introduction to Geogebra” tutorial before proceeding further.

Slide Number 2 Please note that the intention to teach this tutorial is not to replace the actual compass box.

Construction in GeoGebra is done with the view to understand the properties.

Slide Number 3

Learning objectives

In this tutorial we will learn to construct


Cyclic quadrilateral

In-circle

Slide Number 4

System Requirement

To record this tutorial I am using

Linux operating system

Ubuntu Version 10.04 LTS

Geogebra Version 3.2.40.0

Slide Number 5

GeoGebra Tools used in this tutorial

We will use the following tools of Geogebra for the construction

  • compass
  • segment between two points
  • circle with center through point
  • polygon
  • perpendicular bisector
  • angle bisector
  • angle
Switch to Geogebra window

Applications>>Education>>Geogebra

Let us open the Geogebra window.

Let us now construct a cyclic quadrilateral.

Click regular polygon tool >> default value 4 >>

click OK >> construct square

Using the “regular polygon” tool click on any two points on the drawing pad.

A dialog box will open with a default value '4'.

click on OK.


A square 'ABCD' is constructed

Click move tool>> tilt to angle angle Using “move” tool

tilt the square to 45^0(degree) angle.

To do this place, the mouse pointer on 'A' or 'B'

Click perpendicular bisector tool>>click point 'A' and 'B' To construct a perpendicular bisector on segment 'AB'

Select “perpendicular bisector” tool,

click on point 'A'

and then on 'B'

Click perpendicular bisector tool>>click segment 'BC' To construct the perpendicular bisector on 'BC',

we will follow the same process.

Select “perpendicular bisector” tool,

click on point 'B'

and then on 'C'

Point to the intersection point>> mark point as 'E' The two perpendicular bisectors intersect at a point .

Let us mark it as 'E'

Click compass tool>> construct circle Using the “compass” tool,

draw a circle with centre as 'E' which passes through C .

The circle will pass through all the vertices of the quadrilateral

Did you know , the cyclic quadrilateral has maximal area among all quadrilaterals having the same sequence of side lengths

Click on file>>Click on "Save As" >>

type "cyclic_quadrilateral" in file name >> click on OK.

Lets save this file now.

Click on file then on "Save As".

I will type the file name as "cyclic_quadrilateral"

and click on save

Click File>> New window Let us now construct an incircle.

I will open a new geogebra window

Click polygon tool>> draw triangle Using the “polygon” tool

click three points on the drawing pad

and draw a triangle 'ABC'

Click angle tool >> measure the angles

Select the “angle” tool and measure the angles 'BAC' , 'CBA' and 'ACB'.

click the points in the same direction.

Draw angle bisectors >> to angles 'BAC' and 'CBA Lets draw angle bisectors to angles 'BAC' and 'CBA' using “angle bisector” tool
Hover the mouse on Point of intersection The two angle bisectors intersect at point .

Mark this point as 'D' .

click "perpendicular line” tool>>draw perpendicular line Using “perpendicular line” tool

draw a perpendicular line through 'AB' which passes through 'D'

Lines meet at 'E' The perpendicular line intersects 'AB' .

Mark it as 'E'

Compass tool>>draw circle

Using the “compass” tool

let us draw a circle with radius 'DE' .

An in-circle is drawn.

With this we come to an end of this tutorial

Slide number 6

summary

In this tutorial we have learnt to draw

cyclic quadrilateral and

In-circle

Slide Number 7

Assignment

Draw triangle ABC

M a point D on BC and join AD

Draw in-circles for each triangles ABC, ABD and CBD of radii r, r1 and r2 resp.

BE is the height h

verify the relationship between r1,r2 and r as (1 -2r1/h)*(1 - 2r2/h) = (1 -2r/h) by moving the vertices of the Triangle ABC

Show the output of the Assignment The output should look like this.
Slide number 8

Acknowledgement

Watch the video available at

http://spoken-tutorial.org /What is a Spoken Tutorial

It summarises the Spoken Tutorial project

If you do not have good bandwidth, you can download and watch it

The Spoken Tutorial Project Team :

Conducts workshops using spoken tutorials

Gives certificates to those who pass an online test

For more details, contact sptutemail@gmail.com

Spoken Tutorial Project is a part

of the Talk to a Teacher project

It is supported by the National Mission on Education through ICT, MHRD, Government of India

More information on this Mission is available at http://spoken-tutorial.org /NMEICT-Intro

Slide Number 9

About the Contributor

This is Madhuri Ganapathi from IIT Bombay signing off

Contributors and Content Editors

Chandrika, Madhurig, Nancyvarkey