Geogebra/C2/SymmetricalTransformationinGeogebra/English
Title of script: Symmetrical Transformation in Geogebra
Author: Neeta Sawant
Keywords: Symmetryline and Rotation, Reflect Object about Line, Rotate Object around Point by Angle, Dilate object from a Point by Factor, Semicircle through Two points, Dilation, Set trace On, video tutorial
Visual Cue  Narration 

Slide Number 1  Hello everybody.
Welcome to this tutorial on Symmetrical Transformation in Geogebra 
Slide Number 2
Learning Objectives 
In this tutorial we will learn Symmetrical transformations such as
and also learn to

Slide Number 3
Prerequisites 
We assume that you have the basic working knowledge of Geogebra
If not, For relevant tutorials on Geogebra. Please visit our website 
Slide Number 4
System Requirement 
To record this tutorial I am using
Ubuntu Linux OS Version 11.10 Geogebra Version 3.2.47.0 
Slide Number 5
GeoGebra Tools used in this tutorial 
We will use the following Geogebra tools

slide Number 6
Definition of Transformation 
Symmetrical transformation of a geometric figure is  A change in its position, size or shape on a coordinate plane Original figure is called 'Object' Transformed figure is called 'Image' 
Slide Number 7
Reflection symmetry 
Reflection symmetry
Is also called as Line symmetry A type of symmetry where one half is the reflection of the other half You could fold the image and have both halves match exactly 
Switch to GeoGebra window
Dash home >>Media Apps>>Under Type >>Education>>Geogebra 
Let's Switch to GeoGebra window
Dash home >>Media Apps>>Under Type >>Choose Education>> and Geogebra 
Click on Close button on Algebric view 
For this tutorial I am closing the Algebric view Click on Close button on Algebric view 
Let's start with “Line of symmetry”  
Click on “Polygon” tool >> To Construct a triangle  First let's construct an equilateral triangletriangle
Select “Regular Polygon” tool from toolbar. 
Click on drawing pad
Points 'A' ,'B' >>enter 3 click Ok 
Click on drawing pad points 'A' ,'B', and enter 3 for the number of sides. An equilateral triangle 'ABC' is drawn 
Select “Perpendicular Bisector Tool” >> click on side AC  Let's draw a perpendicular bisector to one of the sides of the triangle
Select “Perpendicular Bisector Tool” and click on side AC 
Select the Point tool >> create a point D
Right click on point D >> select Trace ON Click on Reflect Object about Line 
Select the Point tool and create a point D .
Move the point D towards one of the vertices . Right click on point D and select Trace ON Select “Reflect Object about Line”tool from the tool bar 
Click on the Point D  Click on the Point D
This will highlight Point D 
Click on perpendicular Bisector  Click on perpendicular Bisector
This will produce reflected image D' on the other side of perpendicular bisector 
'D is mirror image of point 'D'
Set Trace On for the point D'  
Let us move the point D along the triangle using Move tool  
Click on the “Move” tool  Click on the first option under Move tool from the toolbar 
Drag the object  Click on figure with the mouse.
Drag it tracing the triangle . Now release the mouse button. What do you notice ? Here perpendicular bisector is the line of symmetry D is the object and D' is the image 
Let's reflect a semicircle about a line  
Click on the “Semicircle through Two points” tool >>Mark points E and F  Let's draw a semicircle
Click on the “Semicircle through Two points” tool Mark point E and F 
Click on Segement Between two points>> Draw a line GH  Click on segment Between two Points
Mark points G and H A line is drawn 
Right click on line GH>>Object properties >>Click on Style>>change Style  Let's change the object properties
Right click on line GH Click on Object properties Click on Style change Style 
Click on Reflect Object about Line  Select “Reflect Object about Line” tool from the toolbar 
Click on the semicircle EF  Click on the semicircle EF
This will highlight the semicircle EF 
Click on line GH  Click on line GH
This will produce the reflected image E'F' on the other side of line GH What does the figure look like now ? It looks like a circle 
Click on "Save As" >> type " Linesymmetry " in file
name >> click on save 
Let us save this file now
Click on “File”>> "Save As" I will type the file name as "Linesymmetry" and click on “Save” 
Next, let us learn “Rotate Object around a Point by Angle”  
Slide Number 9
Definition of Rotation 
Definition of Rotation
A rotation is a transformation that turns a figure around a fixed center by an angle If the figure appears unchanged, then the figure has rotation symmetry You can rotate object at any degree measure Rotation can be clockwise and counterclockwise 
Click on “File” >> New  Let's open a new Geogebra window
click on “File” >> New 
Click on “Polygon” tool >> To Construct a Square  Let us construct a square 'ABCD'
click on “Regular Polygon” tool from the toolbar 
Click on drawing pad and mark points 'A' and 'B'  Click on the drawing pad
Mark points 'A' and 'B' 
A dialog box opens
Click OK 
A dialog box opens
Click on OK A square 'ABCD' is drawn 
Click on Rotate Object around a Point by Angle  Click on “Rotate Object around a Point by Angle” tool 
Click on the Square 'ABCD'  Click on the Square 'ABCD'
This will highlight the square 
Click on the point  Next Click on any one of the vertices
I will click on 'A' 
A dialog box opens  A dialog box opens 
Type "60" in Angle field  Type “60” in the Angle field 
Select "°" from first drop down list  Select "°" from first drop down list 
Select the option "Clockwise"  Select the option “clockwise” 
Click on OK  Click on OK
This will rotate the square clockwise at the point of selection with the angle of 60 The rotated image 'A`B`C` 'D' is formed 
Let's move this figure aside using Move tool  
Next, let's “Dilate or enlarge object from point by factor”  
Slide Number 10
Dilation 
Dilation

Draw a triangle 'ABC'  Let's draw a triangle Using the “Polygon”tool
E , F , G click on E again to complete the triangle 
Click on New point tool>>Mark point 'H'  Click on New point tool and
Mark a point 'H' 
Click on Dilate Object from Point by Factor tool  Click on “Dilate Object from Point by Factor” tool 
Click on triangle 'EFG  Click on the triangle 'EFG'
This will highlight the triangle 
Click on a point 'H'  Click on the point 'H' 
A dialog box opens  A dialog box opens 
Type "2">>click OK  Type 2 in the number field
Click on OK 
This will dilate or enlarge the object twice  
Click on Segement Between two Points >> join points  Click on Segement Between two Points tool
join points H,E,E' join points H,G,G' join points H,F,F' 
Here you can see that H is the point of dilation
You can enlarge object as number of times as you wish, by typing the value of Factor  
Click on "Save As" >> type " Dilatetriangle " in file
name >> click on save 
Let us save this file now
Click on “File”>> "Save As" I will type the file name as "Dilatetriangle" Click on “Save” with this we come to the tutorial 
Slide Number 11
Summary 
Let's summarize
In this tutorial we learnt

Slide Number 12
Assignment 
As an assignment I would like you to Draw a Pentagon Use Regular Polygon tool to draw(Hint:sides=5) Draw a Perpendicular bisector to one of the sides of the pentagon Create a point in side the pentagon Set trace On for the point Get reflection of the point about the perpendicular bisector Set trace On for the image point Trace the pentagon to see if you have selected the correct line of symmetry Rotate the original pentagon counter clockwise in 135° at a point Dilate the pentagon at a point by the factor of 3 
Show the output of the Assignment  The assignment should look like this 
Slide number 13
Acknowledgement 
Watch the video available at 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, please write to contact@spokentutorial.org  
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://spokentutorial.org/NMEICTIntro This is Neeta Sawant from SNDT Mumbai signing off. Thanks for joining 