| Slide Number 1
|Welcome to this tutorial on Types of Symmetry in GeoGebra.|
| Slide Number 2
| In this tutorial we will learn about various types of symmetry like:
| Slide Number 3
| To record this tutorial, I am using,
Ubuntu Linux OS version 14.04
GeoGebra version 5.0.438.0-d.
| Slide Number 4
| 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
| A geometric figure is symmetric, if
|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
| 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.
|| 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.
|| 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
| Now let us learn about rotational symmetry.
An object has rotational symmetry, if
|Click on File >> New Window.|| Let us open a new GeoGebra 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
| As an assignment,
|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
| 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
| As an assignment,
| Slide Number 10
| 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 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
| 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
| Let us summarise what we have learnt.
In this tutorial we have learnt about
Symmetry and various types of symmetry
| Slide Number 13
About Spoken Tutorial project
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Please download and watch it.
| Slide Number 14
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| Slide Number 15
Forum for specific questions:
Do you have questions in THIS Spoken Tutorial?
|Please post your timed queries in this forum.|
| Slide Number 16
| 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.