Difference between revisions of "Geogebra/C2/Symmetrical-Transformation-in-Geogebra/English-timed"

!'''Time'''

!'''Narration'''

|Hello everybody.Welcome to this tutorial on Symmetrical Transformation in Geogebra  

|In this tutorial we will learn Symmetrical transformations such as

|Line symmetry  

 

|Rotation symmetry  

|and also learn to

Enlarge figure with scale and position  

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

|If not, For relevant tutorials, Please visit our website

|To record this tutorial I am using

Ubuntu Linux OS Version 11.10

|Geogebra Version 3.2.47.0  

|We will use the following Geogebra tools

|Regular Polygon and  

|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'''  

|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  

|Let's Switch to GeoGebra window

|Look on Dash home >>Media Apps>>Under Type >>Choose Education>> and Geogebra

|For this tutorial I am closing the Algebric view

|Click on Close button on Algebric view

|Let's start with '''Line of symmetry'''

|First let's construct an equilateral triangle.

|Select “Regular Polygon” tool from the toolbar.  

|An equilateral triangle '''ABC''' is drawn  

|Let's draw a perpendicular bisector to one of the sides of triangle

|Select '''Perpendicular Bisector Tool''' and click on side AC  

|Select the Point tool and create a point inside the triangle.

|Right click on point D and select Trace ON

|Select '''Reflect Object about Line'''tool from the tool bar  

|Click on the point D

 

|This will highlight Point D

|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 first option under Move tool from the toolbar

|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

|Let's draw a semicircle

 

|Click on the '''Semicircle through Two points''' tool Mark point E and then F  

|Click on segment Between two Points

|Mark points G and H A line is drawn  

|Let's change the property of the line

|4:08

|Right click on the line Object properties Click on Style change Style  

|Select '''Reflect Object about Line''' tool from the toolbar

|Click on the semicircle EF

|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  

|Let us save this file now

|Click on '''File'''>> '''Save As'''

|I will type the file name as '''Line-symmetry''' and click on '''Save'''

|Next, let us learn to '''Rotate the Object around a Point by Angle'''

|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  

|Let's open a new Geogebra window

|click on '''File''' >> New

|click on '''Regular Polygon''' tool from the toolbar  

|Click on the drawing pad

|Mark points '''A''' and '''B'''  

|A dialog box opens

|Click on OK

|A square '''ABCD''' is drawn  

|Click on '''Rotate Object around a Point by Angle''' tool

|Click on the Square '''ABCD'''

|This will highlight the square

|Next Click on any one of the vertices

|I will click on '''A'''

|A dialog box opens

|Type '''60''' in the Angle field

|Select '''"°"''' from first drop down list

|Select the option '''clockwise'''

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'''  

|Dilation

|in which a figure is enlarged using a scale factor  

|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 and

|Mark a point '''H'''  

|Click on '''Dilate Object from Point by Factor''' tool  

|Click on the triangle '''EFG'''

|This will highlight the triangle  

|Click on the point 'H'

|A dialog box opens

|Type value of 2 in the number field

|Click on OK

|This will dilate or enlarge the object twice

|Click on Segment Between two Points, 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  

|Let us save this file now

|Click on '''File'''>> '''Save As'''

|I will type the file name as '''Dilate-triangle'''

|Click on '''Save''' with this we come to the end of this tutorial  

|Let's summarize

|In this tutorial we learnt

|Reflection about a line  

|Rotation of an object at a point  

|Enlargement of an object by a scale factor  

|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

|The assignment should look like this

|Watch the video available at this URL

|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 the spoken tutorials

|Gives certificates to those who pass an online test

|For more details, please write to

contact@spoken-tutorial.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

|This is Neeta Sawant from SNDT University Mumbai signing off.