View source for GeoGebra-5.04/C2/Types-of-Symmetry/English

{|border=1
||'''Visual Cue'''
||'''Narration'''
|-

|| '''Slide Number 1''' 

'''Title slide''' 
|| Welcome to this tutorial on '''Types of Symmetry''' in '''GeoGebra'''. 

|- 
|| '''Slide Number 2''' 

'''Learning Objectives''' 
|| In this tutorial we will learn about various types of symmetry like: 

* Line 

* Point 

* Rotation 

* Translational 

* Scale 

|- 
|| '''Slide Number 3''' 

'''System Requirement''' 
|| To record this tutorial, I am using, 

'''Ubuntu Linux''' OS version 14.04 

'''GeoGebra''' version 5.0.438.0-d. 

|- 
|| '''Slide Number 4''' 

'''Pre-requisites''' 

'''www.spoken-tutorial.org''' 
|| To follow this tutorial, you should be familiar with, the '''Geogebra''' interface. 

If not, for relevant '''GeoGebra''' tutorials please visit our website. 
|- 
|| 
|| Let us begin with the definition of symmetry. 

|- 
|| '''Slide Number 5''' 

'''Symmetry ''' 
|| A geometric figure is symmetric, if 
* it can be divided into two or more identical parts 
* and its parts can be arranged in an organized manner. 

|- 
|| Cursor on '''GeoGebra''' window. 
|| I have already opened the '''GeoGebra''' interface. 

|- 
||Cursor '''Graphics view'''. 
|| For this tutorial I will uncheck the axes. 

|- 
|| Right-click on '''Graphics view'''. 

'''Graphics''' menu appears. 

In the menu uncheck '''Axes''' check box. 
|| To do so, right-click on the '''Graphics''' view. 

The '''Graphics''' menu appears. 

In this menu, uncheck the '''Axes''' check box. 
|- 
|| Point to all the tools. 
|| In this tutorial, we use all the tools available under the '''Reflect about Line''' tool. 

|- 
|| '''Slide Number 6''' 

'''Line Symmetry''' 
|| Now we will define line symmetry.

A figure has line symmetry, 

if one half of the object is the mirror image of the other half. 

The line over which the figure is reflected is called the line of symmetry.
|- 
|| Click on '''Segment ''' tool >> click on '''Graphics view'''. 

Move the cursor to point '''A'''. 
|| To draw a vertical line '''AB''', click on the '''Segment''' tool and then on '''Graphics view'''. 

Point '''A''' is drawn in the '''Graphics view'''. 

|- 
|| Click again. 

Point to segment '''AB'''. 
|| Click again directly below point '''A''' to draw segment '''AB'''. 

Note that it is labelled as '''f'''. 

|- 
|| Select '''Semicircle through 2 Points ''' tool. 
|| Select the '''Semicircle through 2 Points''' tool. 

|- 
|| Click on left-side of segment '''AB'''. 

Point to point '''C'''. 
|| Click on the left-side of segment '''AB'''. 

Point '''C''' is drawn. 

|- 
|| Click again at a different place. 

Point to the semicircle '''c'''. 

|| Click again below '''C''' to complete the semicircle '''CD''' named as '''c.''' 

This semicircle should be to the left of segment '''f'''. 

|- 
|| Point to semicircle '''c''' and line '''f'''. 
|| Now let us reflect the semicircle about the segment '''f'''.

|- 
|| Click on '''Reflect about Line''' tool >> 

Click semicircle >> line '''f'''. 
|| Click on the '''Reflect about Line''' tool. 

Click on the semicircle, then on line '''f'''. 

|- 
|| Point to the reflected semicircle '''c''''. 
|| Semicircle '''c''''(c prime) appears on the right side of segment '''f'''. 

It is a reflected image of semicircle '''c'''. 

|- 
|| Point to '''c''' and '''c' ''' .
|| Let's change the object properties of '''c''' and '''c''''(c prime).

|- 
|| Right-click on '''c ''' >> select '''Object Properties'''. 
|| Right-click on '''c''' and select '''Object Properties'''. 

|- 
|| Point to '''Preferences''' window. 
|| '''Preferences''' window opens. 

|- 
|| Point to '''Conic'''. 
|| In the left panel under '''Conic''', '''c''' is already selected. 

|- 
|| Press the '''Ctrl''' key>> click on '''c' '''. 
|| While holding the '''Ctrl''' key, click on '''c''''(c prime). 

|- 
|| Point to '''Basic''' tab >> click '''Show Trace''' check box. 
|| In the '''Basic''' tab, click the '''Show Trace''' check box. 

|- 
|| Click on '''Color''' tab >> click on pink. 


Click on X button. 
|| In the '''Color '''tab, I will  choose the colour as pink. 

You may choose any colour of your choice. 

Then close the '''Preferences''' window. 

|- 
|| Click on '''Move''' tool >> drag point '''C'''. 

|| Using the '''Move''' tool, drag the semicircle '''c''' .
|- 
|| Point to '''c''' and '''c''''.
|| Observe that semicircle '''c''''(c prime) moves as we move ''' c'''. 

|- 
|| Point to '''c''' and '''c' '''. 
|| '''c''''(c prime) is the mirror image of '''c''', with segment '''f''' as the mirror. 

|- 
|| Click on '''Move Graphics View''' tool >> drag '''Graphics view'''. 
|| To erase the traces, drag the '''Graphics view'''. 

|- 
|| Cursor on '''Graphics view'''. 


Press '''Ctrl A''' to select  >> Press '''Delete''' key. 
|| Let us delete all the objects in the '''Graphics view'''. 

Press '''Ctrl + A ''' keys to select all the objects. 

Then press the '''Delete''' key on the keyboard. 

|- 
|| Cursor on the '''Graphics view'''. 
|| Now let us learn to reflect about a point. 

|- 
|| Click on '''Segment ''' tool. 

Click on '''Graphics view ''' twice. 
|| Click on '''Segment ''' tool. 

Click within the '''Graphics view''' twice to draw a segment '''AB'''. 

|- 
|| Select '''Refect about Point''' tool. 

Click on point '''A '''  >> click on point  '''B'''. 
|| Select the '''Reflect about Point''' tool. 

Click on point '''A''', then on point '''B'''. 
|- 
|| Point to the reflected image '''A' '''. 
|| '''A''''(A prime)which is the reflected image of '''A''',  appears on the otherside of point '''B'''. 

|- 
|| Drag the '''Graphics view'''. 
|| To view '''A' '''(A prime), drag the '''Graphics view''' if required. 

|- 
|| Point to '''A''' and '''A'''' 
|| To show that '''A''''(A prime) is the image of '''A''', we will measure the distances '''AB''' and '''A''''(A prime)'''B'''. 
|- 
|| Click on '''Distance or Length '''tool. 
|| Under '''Angle''', click on the '''Distance or Length''' tool. 

|- 
|| Click on A >> click on B. 
|| Click on point '''A''', then on '''B'''. 

|- 
|| click on '''A' ''' >> click '''B'''. 
|| Again click on '''A'''' (A prime) and then on '''B'''. 

|- 
|| Point to the distances '''AB''' and '''A'B'''.
|| Notice that the distances '''AB''' and '''A''''(A prime)'''B ''' are equal. 

|- 
|| Click on '''Move''' tool >>drag '''AB'''. 
|| Using '''Move''' tool, I will drag segment '''AB''' upwards. 

|- 
|| Point to moved objects. 
|| Observe that '''A''''(A prime) also moves along with '''AB'''. 

|- 
|| Cursor on Graphics view. 
|| Next we will learn to reflect a point about a circle. 

|- 
|| Click on '''Circle with centre and Radius''' tool. 
|| Select the''' Circle with centre and radius '''tool. 

|- 
|| Click on the '''Graphics view.''' 
|| Click within the '''Graphics view'''. 

|- 
|| Point to the text box. 
|| The '''Circle with Centre and Radius''' text box appears. 

|- 
|| Type 2 >> click '''OK''' button. 
|| In the text box type ''' Radius''' as 2 and click on the '''OK''' button at the bottom. 

|- 
|| Point to the drawn circle and center '''C'''. 
|| A circle with centre '''C''' and radius 2 cm is drawn in the '''Graphics view'''. 

|- 
|| Click on '''Point''' tool >> click outside the circle. 
|| Using '''Point''' tool, draw a point '''D''' outside the circle. 

|- 
|| Select '''Reflect about Circle''' tool. 
|| Select the''' Reflect about Circle''' tool. 

|- 
|| Click on the point '''D''' >> click on circle '''c'''. 
|| Click on point '''D''' and then click on circle '''c'''. 
|- 
|| Point to '''D''''
|| '''D''''(D prime), which is the image of '''D''', appears inside the circle. 

|- 
|| Click on '''Move''' tool and drag the point '''D'''. 
|| Click on the '''Move''' tool and drag point '''D''' around the circle. 
|- 
|| Point to '''D'''' and '''D'''. 
|| Observe that '''D''''(D prime) also moves inside the circle mirroring '''D'''. 

|- 
|| Drag point '''D''' inside circle. 

Point to '''D''' and '''D'''' 
|| Drag point '''D''' inside the circle and see what happens. 

'''D''' and '''D''''(D prime)exchange places. 

|- 
|| '''Slide Number 7''' 

'''Rotational Symmetry''' 
|| Now let us learn about rotational symmetry. 

An object has rotational symmetry, if 

* it can be rotated about a fixed point 
* without changing the overall shape. 
|- 
|| Click on '''File '''>> '''New Window'''. 
|| Let us open a new '''GeoGebra''' window. 


Click on ''' File ''' and then on '''New Window'''. 

|- 
|| Cursor on '''Graphics view'''. 
|| We will now rotate an object around a point. 

For this, I will draw a square. 
|- 
|| Click on '''Polygon''' tool. 

Click on Graphics view to draw point '''A'''. 

Click to draw point '''B''', '''C''' and '''D'''. 

Click on '''A'''. 
|| Click on the '''Polygon''' tool. 

Click within the '''Graphics view''' to draw point '''A'''. 

Similarly click to draw points '''B''', '''C''' and '''D'''. 

To complete the polygon click again on point '''A'''. 

|- 
|| Point to quadrilateral '''ABCD'''. 
|| A quadrilateral '''ABCD''' named as '''q1''' is drawn. 

|- 
|| Cursor on '''quadrilateral q1'''. 

Click on '''Move''' tool >> drag the points. 
|| To convert '''q1''' to a square, we have to adjust the lengths. 

Click on the '''Move''' tool and drag the points '''A''', '''B''', '''C''' and '''D'''. 

|- 
|| Point to the lengths in '''Algebra View'''. 

a=3, b=3, c=3,d=3. 
|| Notice the change in the lengths in the '''Algebra view'''. 

All the lengths have to be same. 

|- 
|| Point to the square. 
|| We will now draw perpendicular bisectors to the square. 

|- 
|| Click on '''Perpendicular Bisector''' tool. 
|| Click on '''Perpendicular Bisector''' tool. 

|- 
|| Click on points '''A''','''B''' and '''B''','''C'''. 

Point to the intersection point. 
|| Click on points '''A''', '''B''' and '''B''', '''C'''. 

The two perpendicular bisectors intersect at a point. 

|- 
|| Click on '''Intersect''' tool >> click on point of intersection. 
|| Click on '''Intersect''' tool and click on point of intersection. 

Point '''E ''' is the point of intersection. 

|- 
|| Click on '''Slider''' tool >> click on the '''Graphics view'''. 
|| Let us create an angle slider. 

Click on '''Slider''' tool and click in the '''Graphics view.''' 
|- 
|| Point to '''Slider ''' dialog box. 
|| The '''Slider '''dialog box appears. 

|- 
|| Select '''Angle''' radio button. 
|| Select '''Angle''' radio button. 

|- 
|| Point to alpha in the '''Name field'''. 
|| '''Alpha''' appears in the '''Name field'''. 

|- 
|| Point to the values. 

Click '''OK''' button. 
|| Leave the default values of '''Min''', '''Max ''' and '''Increment''' as they are. 

And click on the '''OK''' button at the bottom. 
|- 
|| Point to alpha slider. 
|| Alpha slider is created in the '''Graphics view'''. 

|- 
|| Click on '''Rotate around Point''' tool. 

Click on square '''ABCD''' >> point '''E'''. 
|| Now click on the '''Rotate around Point''' tool. 

Click on the square '''q1''' and then point '''E'''. 

|- 
|| Point to the text box and Angle value. 
|| '''Rotate around Point''' text box appears with 45 degrees angle. 

|- 
|| Point to '''counter clockwise''',  '''clockwise''' radio buttons. 

Point to '''clockwise.''' 
|| Below the text box we have, '''counter clockwise''' and '''clockwise''' radio buttons. 

You can select any one of the radio buttons as per your choice. 

I will select '''clockwise'''. 

|- 
|| Delete 45 degrees from '''Angle''' text box. 
|| Delete 45 degrees from the '''Angle''' text box. 

|- 
|| Point to alpha symbol on the right-side. 



|| In the '''Angle''' text box, notice an alpha symbol on the rightside. 

|- 
|| Click to show table of symbols. 
|| Click on it to show the table of symbols. 

|- 
|| Select '''alpha''' from the table >> click '''OK''' button. 
|| Select '''alpha''' from the table and click on the '''OK''' button at the bottom. 

|- 
|| Point to square '''q1'''' on the Graphics view. 
|| Observe that a new square '''q1'''' appears in the '''Graphics view'''. 

This square '''q1' ''' is rotated at angle alpha with respect to square '''q1'''. 

|- 
|| Drag the '''alpha''' slider between 0 degrees to 360 degrees. 
|| Now drag the '''alpha''' slider between 0 degrees to 360 degrees. 

As we drag, notice the rotation of '''q1'''' around the point '''E'''. 

|- 
|| '''Slide Number 8'''

'''Assignment '''
|| As an assignment, 

* Draw a hexagon and show its rotation symmetry. 
|- 
|| Cursor on '''Graphics view'''. 
|| Let us now delete all the objects. 

|- 
|| Go '''Edit''' menu >> navigate to '''Select All'''. 

Select''' Delete '''option. 
|| Go to '''Edit''' menu and navigate to '''Select All'''. 

Then select the '''Delete''' option. 
|- 
|| 
|| Next we will move an object using a vector. 

|- 
|| '''Slide Number 9 '''

'''Translational symmetry '''
|| Let us define translational symmetry 
 
An object has '''translational''' symmetry if, it can be moved without changing its overall shape. 

|- 
|| Click on ''Polygon''' tool>>click on points '''ABC'''. 
|| Using the '''Polygon''' tool draw a triangle '''ABC''' named as '''t1'''. 

|- 
|| Click on '''Line''' tool drop-down>>Select '''Vector''' tool. 
|| To draw a vector, click on the''' Vector''' tool from the tool bar. 

|- 
|| Click on point '''D''' >> point '''E'''. 
|| Click on point '''D''' and then on point '''E'''. 

|- 
|| Point to '''u'''. 
|| The vector is represented by''' u.''' 

|- 
|| Click on '''Translate by Vector''' tool. 

Click on '''t1''' >> on vector '''u'''. 
|| Select '''Translate by Vector ''' tool. 

Click on the triangle '''t1''' and then on the vector '''u'''. 

|- 
|| Point to the translated image. 

Point to '''t1''' and '''t1' '''. 
|| Here '''t1' ''' is the translated image of '''t1'''. 

The distance between '''t1''' and '''t1' '''is exactly same as the length of vector '''u'''. 
|- 
|| Click on '''Move''' tool>> drag vector '''u'''. 

Point to the image triangle. 
|| Using the '''Move''' tool, drag point '''E''' of the vector '''u'''. 

Observe that the image triangle '''t1'''' translates along with vector '''u'''. 
|- 
|| '''Slide Number 9'''

'''Assignment''' 
|| As an assignment, 

* Draw a vector.

* Translate a point using '''Translate by Vector''' tool.

* Measure the distance between the original point and the translated point. 
|- 
|| '''Slide Number 10''' 

'''Scale Symmetry''' 
|| Let us define scale symmetry. 

An object has '''scale''' symmetry if, 

it does not change shape when it is expanded or contracted. 

|- 
|| Cursor on '''Graphics view'''. 

Click on '''File''' >> select '''New Window'''. 
|| Let us open a new Geogebra window. 

Click on '''File''' and select '''New Window'''. 

|- 
|| Cursor on '''Graphics view'''. 
|| Now let us learn how to dilate an object.

|- 
|| Click on '''Circle with centre and radius''' tool. 


Click on '''Graphics view'''. 
|| Click on the '''Circle with centre and radius '''tool. 

Then click on the '''Graphics view'''. 

|- 
|| Type radius as 1 in '''Circle with Centre and Radius''' text box. 
|| Type radius as 1 in the '''Circle with Centre and Radius''' text box. 

|- 
|| Click '''OK'''. 
|| Click on '''OK ''' button at the bottom. 

|- 
|| Click on '''Point''' >> click outside the circle. 
|| Using '''Point''' tool draw a point '''B''' outside the circle. 
|- 
|| Click on '''Dilate from Point''' tool. 

Click on circumference >> click on '''B'''. 
|| Select the '''Dilate from Point''' tool. 

Click on the circumference of the unit circle then click on point '''B'''. 
|- 
|| Point to the box. 

Type 2 as factor >> click '''OK''' button. 
|| The '''Dilate from Point''' text box appears. 

Type the '''Factor''' as 2 and click on the '''OK''' button at the bottom. 

|- 
|| Point to the new circle. 
|| A dilated circle with double the radius appears in the '''Graphics view'''. 

|- 
|| '''Slide Number 11''' 

'''Assignment'''. 
|| As an assignment,

Draw a pentagon and a hexagon on the same window. 

Dilate the pentagon by a factor of 0.5 

Dilate the hexagon by a factor of 3. 

|- 
|| '''Slide Number 12''' 

'''Summary''' 
|| Let us summarise what we have learnt. 

In this tutorial we have learnt about 

Symmetry and various types of symmetry 

* Line 
* Point 
* Rotation 
* Translational 
* Scale. 
|- 
|| '''Slide Number 13''' 

'''About Spoken Tutorial project''' 
|| The video at the following link summarises the Spoken Tutorial project. 

Please download and watch it. 

|- 
|| '''Slide Number 14''' 

'''Spoken Tutorial workshops''' 
|| The '''Spoken Tutorial Project '''team, conducts workshops and gives certificates. 

For more details, please write to us. 

|- 
|| '''Slide Number 15''' 

'''Forum for specific questions:''' 

Do you have questions in THIS '''Spoken Tutorial'''? 

* Please visit this site

* Choose the minute and second where you have the question.

* Explain your question briefly

* Someone from our team will answer them. 

|| Please post your timed queries in this forum. 

|- 
|| '''Slide Number 16''' 

'''Acknowledgement''' 
|| Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India. 

More information on this mission is available at this link. 

|- 
|| 
|| This is Madhuri Ganapathi from, IIT Bombay signing off. 

Thank you for watching. 
|-
|}