Difference between revisions of "Geogebra/C2/Symmetrical-Transformation-in-Geogebra/English-timed"
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Revision as of 14:54, 11 August 2014
| Time | Narration |
|---|---|
| 00:00 | Hello everybody.Welcome to this tutorial on Symmetrical Transformation in Geogebra |
| 00:06 | In this tutorial we will learn Symmetrical transformations such as |
| 00:11 | Line symmetry |
| 00:12 | Rotation symmetry |
| 00:13 | and also learn to
Enlarge figure with scale and position |
| 00:17 | We assume that you have the basic working knowledge of Geogebra |
| 00:21 | If not, For relevant tutorials, Please visit our website |
| 00:26 | To record this tutorial I am using
Ubuntu Linux OS Version 11.10 |
| 00:31 | Geogebra Version 3.2.47.0 |
| 00:35 | We will use the following Geogebra tools |
| 00:37 | Reflect Object about Line |
| 00:39 | Rotate Object around Point by Angle |
| 00:42 | Dilate object from a Point by Factor |
| 00:45 | Semicircle through Two points |
| 00:47 | Regular Polygon and |
| 00:49 | Perpendicular bisector |
| 00:51 | Definition of Transformation |
| 00:53 | Symmetrical transformation of a geometric figure is - |
| 00:57 | A change in its position, size or shape on a coordinate plane |
| 01:02 | Original figure is called 'Object' |
| 01:04 | Transformed figure is called 'Image' |
| 01:07 | Reflection symmetry |
| 01:09 | Is also called as Line symmetry |
| 01:11 | A type of symmetry where one half is the reflection of the other half |
| 01:15 | You could fold the image and have both halves match exactly |
| 01:20 | Line of Symmetry is the line over which the figure is reflected. |
| 01:24 | Let's Switch to GeoGebra window |
| 01:27 | Look on Dash home >>Media Apps>>Under Type >>Choose Education>> and Geogebra |
| 01:37 | For this tutorial I am closing the Algebric view |
| 01:40 | Click on Close button on Algebric view |
| 01:47 | Let's start with “Line of symmetry” |
| 01:50 | First let's construct an equilateral triangle. |
| 01:53 | Select “Regular Polygon” tool from the toolbar. |
| 01:57 | Click on drawing pad points 'A' ,'B', and enter 3 for the number of sides. |
| 02:08 | An equilateral triangle 'ABC' is drawn |
| 02:11 | Let's draw a perpendicular bisector to one of the sides of triangle |
| 02:15 | Select “Perpendicular Bisector Tool” and click on side AC |
| 02:26 | Select the Point tool and create a point inside the triangle. |
| 02:31 | Move the point D towards one of the vertices . |
| 02:38 | Right click on point D and select Trace ON |
| 02:43 | Select “Reflect Object about Line”tool from the tool bar |
| 02:48 | Click on the point D |
| 02:49 | This will highlight Point D |
| 02:52 | Click on perpendicular Bisector |
| 02:55 | This will produce reflected image D' on the other side of perpendicular bisector |
| 03:01 | 'D is mirror image of point 'D' |
| 03:04 | Set Trace On for the point D' |
| 03:08 | Let us move the point D along the triangle using Move tool |
| 03:11 | Click on the first option under Move tool from the toolbar |
| 03:22 | Click on figure with the mouse. |
| 03:25 | Drag it tracing the triangle . |
| 03:28 | Now release the mouse button. |
| 03:31 | What do you notice ? |
| 03:32 | Here perpendicular bisector is the line of symmetry |
| 03:36 | D is the object and D' is the image |
| 03:39 | Let's reflect a semicircle about a line |
| 03:43 | Let's draw a semicircle |
| 03:44 | Click on the “Semicircle through Two points” tool Mark point E and then F |
| 03:56 | Click on segment Between two Points |
| 04:02 | Mark points G and H A line is drawn |
| 04:06 | Let's change the property of the line |
| 4:08 | Right click on the line Object properties Click on Style change Style |
| 04:21 | Select “Reflect Object about Line” tool from the toolbar |
| 04:27 | Click on the semicircle EF |
| 04:31 | Click on line GH |
| 04:34 | 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 |
| 04:45 | Let us save this file now |
| 04:47 | Click on “File”>> "Save As" |
| 04:50 | I will type the file name as "Line-symmetry" and click on “Save” |
| 05:05 | Next, let us learn to “Rotate the Object around a Point by Angle” |
| 05:12 | Definition of Rotation |
| 05:15 | A rotation is a transformation that turns a figure around a fixed center by an angle |
| 05:21 | If the figure appears unchanged, then the figure has rotation symmetry |
| 05:29 | You can rotate object at any degree measure Rotation can be clockwise and counterclockwise |
| 05:39 | Let's open a new Geogebra window |
| 05:41 | click on “File” >> New |
| 05:47 | Let us construct a square. |
| 05:49 | click on “Regular Polygon” tool from the toolbar |
| 05:55 | Click on the drawing pad |
| 05:57 | Mark points 'A' and 'B' |
| 05:59 | A dialog box opens |
| 06:01 | Click on OK |
| 06:03 | A square 'ABCD' is drawn |
| 06:05 | Click on “Rotate Object around a Point by Angle” tool |
| 06:13 | Click on the Square 'ABCD' |
| 06:16 | This will highlight the square |
| 06:18 | Next Click on any one of the vertices |
| 06:20 | I will click on 'A' |
| 06:23 | A dialog box opens |
| 06:25 | Type “60” in the Angle field |
| 06:30 | Select "°" from first drop down list |
| 06:35 | Select the option “clockwise”
Click on OK |
| 06:40 | This will rotate the square clockwise at the point of selection with the angle of 60° |
| 06:44 | The rotated image 'A`B`C` 'D' is formed |
| 06:49 | Let's move this figure aside using Move tool |
| 07:00 | Next, let's “Dilate or enlarge object from point by factor” |
| 07:09 | Dilation |
| 07:11 | Dilation or enlargement is a transformation |
| 07:14 | in which a figure is enlarged using a scale factor |
| 07:23 | Let's draw a triangle Using the “Polygon”tool |
| 07:28 | E , F , G click on E again to complete the triangle |
| 07:36 | Click on New point tool and |
| 07:40 | Mark a point 'H' |
| 07:44 | Click on “Dilate Object from Point by Factor” tool |
| 07:51 | Click on the triangle 'EFG' |
| 07:54 | This will highlight the triangle |
| 07:55 | Click on the point 'H' |
| 07:57 | A dialog box opens |
| 08:00 | Type value of 2 in the number field |
| 08:04 | Click on OK |
| 08:09 | This will dilate or enlarge the object twice |
| 08:16 | Click on Segment Between two Points, join points H,E,E' |
| 08:33 | join points H,G,G' |
| 09:01 | join points H,F,F' |
| 09:15 | Here you can see that H is the point of dilation |
| 09:21 | You can enlarge object as number of times as you wish, by typing the value of Factor |
| 09:28 | Let us save this file now |
| 09:30 | Click on “File”>> "Save As" |
| 09:33 | I will type the file name as "Dilate-triangle" |
| 09:48 | Click on “Save” with this we come to the end of this tutorial |
| 09:55 | Let's summarize |
| 09:58 | In this tutorial we learnt |
| 10:00 | Reflection about a line |
| 10:02 | Rotation of an object at a point |
| 10:05 | Enlargement of an object by a scale factor |
| 10:09 | As an assignment I would like you to |
| 10:11 | Draw a Pentagon |
| 10:12 | Use Regular Polygon tool to draw(Hint:sides=5) |
| 10:17 | Draw a Perpendicular bisector to one of the sides of the pentagon |
| 10:21 | Create a point in side the pentagon |
| 10:25 | Set trace On for the point |
| 10:27 | Get reflection of the point about the perpendicular bisector |
| 10:31 | Set trace On for the image point |
| 10:34 | Trace the pentagon to see if you have selected the correct line of symmetry |
| 10:44 | Rotate the original pentagon counter clockwise in 135° at a point |
| 10:49 | Dilate the pentagon at a point by the factor of 3 |
| 10:56 | The assignment should look like this |
| 11:03 | Watch the video available at this URL |
| 11:06 | It summarises the Spoken Tutorial project |
| 11:09 | If you do not have good bandwidth,you can download and watch it |
| 11:12 | The Spoken Tutorial Project Team :
Conducts workshops using the spoken tutorials |
| 11:17 | Gives certificates to those who pass an online test |
| 11:20 | For more details, please write to
contact@spoken-tutorial.org |
| 11:26 | Spoken Tutorial Project is a part of the Talk to a Teacher project |
| 11:29 | It is supported by the National Mission on Education through ICT, MHRD, Government of India |
| 11:35 | More information on this Mission is available at this link. |
| 11:39 | This is Neeta Sawant from SNDT University Mumbai signing off.
Thanks for joining |
Contributors and Content Editors
Madhurig, Minal, Mousumi, PoojaMoolya, Pratik kamble, Sandhya.np14
