GeoGebra-5.04/C2/Types-of-Symmetry/English-timed

Time	Narration
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: Line Point
00:15	Rotation Translational Scale
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 Line Point
13:56	Rotation Translational Scale.
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