|00:01||Welcome to this tutorial on Types of Symmetry in GeoGebra.|
|00:06||In this tutorial we will learn about various types of symmetry like:
|00:22|| To record this tutorial, I am using,
Ubuntu Linux OS version 14.04
GeoGebra version 5.0.438.0-d.
|00:36|| To follow this tutorial, you should be familiar with, the Geogebra interface.
If not, for relevant GeoGebra tutorials please visit our website.
|00:49||Let us begin with the definition of symmetry.|
|00:53||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.|
|01:08||I have already opened the GeoGebra interface.|
|01:12||For this tutorial I will uncheck the axes.|
|01:16|| To do so, right-click on the Graphics view.
The Graphics menu appears.
|01:23||In this menu, uncheck the Axes check box.|
|01:27||For this tutorial, we will use all the tools available under the Reflect about Line tool.|
|01:35||Now we will define line symmetry.|
|01:38||A figure has line symmetry, if one half of the object is the mirror image of the other half.|
|01:46||The line over which the figure is reflected is called the line of symmetry.|
|01:52||To draw a vertical line AB, click on the Segment tool and then click on Graphics view.|
|02:00||Point A is drawn in the Graphics view.|
|02:04|| Click again directly below point A to draw segment AB.
Note that it is labelled as f.
|02:13||Select the Semicircle through 2 Points tool.|
|02:17||Click on the left-side of segment AB. Point C is drawn.|
|02:24||A gain click below C to complete the semicircle CD named as c.|
|02:30||This semicircle should be to the left of segment f.|
|02:35||Now let us reflect the semicircle about the segment f.|
|02:40||Click on the Reflect about Line tool. Click on the semicircle, then click on line f.|
|02:50||Semicircle c'(c prime) appears on the right side of segment f. It is a reflected image of semicircle c.|
|03:00||Let's change the object properties of c and c'(c prime).|
|03:05||Right-click on c and select Object Properties.|
|03:11||Preferences window opens.|
|03:14||In the left panel under Conic, c is already selected.|
|03:19||While holding the Ctrl key, click on c'(c prime).|
|03:23||In the Basic tab, click the Show Trace check box.|
|03:28||In the Color tab, I will choose the colour as pink.|
|03:33||You may choose any colour of your choice. Then close the Preferences window.|
|03:40||Using the Move tool, drag the semicircle c .|
|03:46||Observe that semicircle c'(c prime) moves as we move c.|
|03:52||c'(c prime) is the mirror image of c, with segment f as the mirror.|
|03:58||To erase the traces, drag the Graphics view.|
|04:03||Let us delete all the objects in the Graphics view.|
|04:07||Press Ctrl + A keys to select all the objects.|
|04:11||Then press the Delete key on the keyboard.|
|04:15||Now let us learn to reflect about a point.|
|04:19||Click on Segment tool.|
|04:22||Click within the Graphics view twice to draw a segment AB.|
|04:28||Select the Reflect about Point tool. Click on point A, then on point B.|
|04:38||A'(A prime)which is the reflected image of A, appears on the otherside of point B.|
|04:45||To view A' (A prime), drag the Graphics view if required.|
|04:50||To show that A'(A prime) is the image of A, we will measure the distances AB and A'(A prime)B.|
|04:58||Under Angle, click on the Distance or Length tool.|
|05:03||Click on point A, then on B.|
|05:08||Again click on A' (A prime) and then on B.|
|05:15||Notice that the distances AB and A'(A prime)B are equal.|
|05:20||Using Move tool, I will drag segment AB upwards.|
|05:27||Observe that A'(A prime) also moves along with AB.|
|05:32||Now we will learn to reflect a point about a circle.|
|05:36||Select the Circle with centre and radius tool. Click within the Graphics view.|
|05:43||The Circle with Centre and Radius text box appears.|
|05:48||In the text box type Radius as 2 and click on the OK button at the bottom.|
|05:56||A circle with centre C and radius 2 cm is drawn in the Graphics view.|
|06:02||Using Point tool, draw a point D outside the circle.|
|06:09||Select the Reflect about Circle tool. Click on point D and then click on circle c.|
|06:19||D'(D prime), which is the image of D, appears inside the circle.|
|06:24||Click on the Move tool and drag point D around the circle.|
|06:31||Observe that D'(D prime) also moves inside the circle mirroring D.|
|06:37||Drag point D inside the circle and see what happens. D and D'(D prime)exchange places.|
|06:47||Now let us learn about rotational symmetry.|
|06:51||An object has rotational symmetry, if it can be rotated about a fixed point without changing the overall shape.|
|07:02||Let us open a new GeoGebra window.|
|07:06||Click on File and then on New Window.|
|07:11||We will now rotate an object around a point. For this, I will draw a square.|
|07:18||Click on the Polygon tool.|
|07:21||Click within the Graphics view to draw point A. Similarly draw points B, C and D.|
|07:33||To complete the polygon click again on point A.|
|07:37||A quadrilateral ABCD named as q1 is drawn.|
|07:42||To convert q1 to a square, we have to adjust the lengths.|
|07:47||Click on the Move tool and drag the points A, B, C and D.|
|07:54||Notice the change in the lengths in the Algebra view. All the lengths have to be same.|
|08:01||We will now draw perpendicular bisectors to the square.|
|08:05||Click on Perpendicular Bisector tool.|
|08:08||Click on points A, B and B, C.|
|08:14||The two perpendicular bisectors intersect at a point.|
|08:18||Click on Intersect tool and click on point of intersection. Point E is the point of intersection.|
|08:28||Let us create an angle slider. Click on Slider tool and click in the Graphics view.|
|08:37||The Slider dialog box appears.|
|08:40||Select Angle radio button.|
|08:43||Alpha appears in the Name field.|
|08:47|| Leave the default values of Min, Max and Increment as they are.
And click on the OK button at the bottom.
|08:58||Alpha slider is created in the Graphics view.|
|09:02||Now click on the Rotate around Point tool. Click on the square q1 and then point E.|
|09:12||Rotate around Point text box appears with 45 degrees angle.|
|09:18||Below the text box we have, counter clockwise and clockwise radio buttons.|
|09:25|| You can select any one of the radio buttons as per your choice.
I will select clockwise.
|09:33||Delete 45 degrees from the Angle text box.|
|09:37||In the Angle text box, notice an alpha symbol on the rightside.|
|09:43||Click on it to show the table of symbols.|
|09:47||Select alpha from the table and click on the OK button at the bottom.|
|09:54||Observe that a new square q1' appears in the Graphics view.|
|10:00||This square q1' is rotated at angle alpha with respect to square q1.|
|10:07||Now drag the alpha slider between 0 degrees to 360 degrees.|
|10:13||As we drag, notice the rotation of q1' around the point E.|
|10:20|| As an assignment,
Draw a hexagon and show its rotation symmetry.
|10:28||Let us now delete all the objects.|
|10:31|| Go to Edit menu and navigate to Select All.
Then select the Delete option.
|10:41||Next we will move an object using a vector.|
|10:45||Let us define translational symmetry|
|10:49||An object has translational symmetry if, it can be moved without changing its overall shape.|
|10:58||Using the Polygon tool draw a triangle ABC named as t1.|
|11:08||To draw a vector, click on the Vector tool from the tool bar.|
|11:13||Click on point D and then on point E.|
|11:19||The vector is represented by u.|
|11:23||Select Translate by Vector tool. Click on the triangle t1 and then on the vector u.|
|11:33||Here t1' is the translated image of t1.|
|11:38||The distance between t1 and t1' is exactly same as the length of vector u.|
|11:45||Using the Move tool, drag point E of the vector u.
Observe that the image triangle t1' translates along with vector u.
|11:59|| As an assignment,
Draw a vector.
|12:04||Translate a point using Translate by Vector tool.|
|12:08||Measure the distance between the original point and the translated point.|
|12:13||Let us define scale symmetry.|
|12:16||An object has scale symmetry if, it does not change shape when it is expanded or contracted.|
|12:25||Let us open a new Geogebra window. Click on File and select New Window.|
|12:34||Now let us learn how to dilate an object.|
|12:38||Click on the Circle with centre and radius tool. Then click on the Graphics view.|
|12:45||Type radius as 1 in the Circle with Centre and Radius text box.|
|12:50||Click on OK button at the bottom.|
|12:53||Using Point tool draw a point B outside the circle.|
|12:59||Select the Dilate from Point tool.|
|13:02||Click on the circumference of the unit circle then click on point B.|
|13:09||The Dilate from Point text box appears. Type the Factor as 2 and click on the OK button at the bottom.|
|13:20||A dilated circle with double the radius appears in the Graphics view.|
|13:26|| As an assignment,
Draw a pentagon and a hexagon on the same window.
|13:32|| Dilate the pentagon by a factor of 0.5
Dilate the hexagon by a factor of 3.
|13:40||Let us summarise what we have learnt.|
|13:44|| In this tutorial we have learnt about
Symmetry and various types of symmetry
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|14:36||This is Madhuri Ganapathi from, IIT Bombay signing off. Thank you for watching.|