Difference between revisions of "Geogebra/C2/Symmetrical-Transformation-in-Geogebra/English-timed"
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|Hello everybody.Welcome to this tutorial on Symmetrical Transformation in Geogebra | |Hello everybody.Welcome to this tutorial on Symmetrical Transformation in Geogebra | ||
|- | |- | ||
− | | | + | |00:06 |
|In this tutorial we will learn Symmetrical transformations such as | |In this tutorial we will learn Symmetrical transformations such as | ||
|- | |- | ||
− | | | + | |00:11 |
|Line symmetry | |Line symmetry | ||
|- | |- | ||
− | | | + | |00:12 |
|Rotation symmetry | |Rotation symmetry | ||
|- | |- | ||
− | | | + | |00:13 |
|and also learn to | |and also learn to | ||
Enlarge figure with scale and position | Enlarge figure with scale and position | ||
|- | |- | ||
− | | | + | |00:17 |
|We assume that you have the basic working knowledge of Geogebra | |We assume that you have the basic working knowledge of Geogebra | ||
|- | |- | ||
− | | | + | |00:21 |
|If not, For relevant tutorials, Please visit our website | |If not, For relevant tutorials, Please visit our website | ||
|- | |- | ||
− | | | + | |00:26 |
|To record this tutorial I am using | |To record this tutorial I am using | ||
Ubuntu Linux OS Version 11.10 | Ubuntu Linux OS Version 11.10 | ||
|- | |- | ||
− | | | + | |00:31 |
|Geogebra Version 3.2.47.0 | |Geogebra Version 3.2.47.0 | ||
|- | |- | ||
− | | | + | |00:35 |
|We will use the following Geogebra tools | |We will use the following Geogebra tools | ||
|- | |- | ||
− | | | + | |00:37 |
|Reflect Object about Line | |Reflect Object about Line | ||
|- | |- | ||
− | | | + | |00:39 |
|Rotate Object around Point by Angle | |Rotate Object around Point by Angle | ||
|- | |- | ||
− | | | + | |00:42 |
|Dilate object from a Point by Factor | |Dilate object from a Point by Factor | ||
|- | |- | ||
− | | | + | |00:45 |
|Semicircle through Two points | |Semicircle through Two points | ||
|- | |- | ||
− | | | + | |00:47 |
|Regular Polygon and | |Regular Polygon and | ||
|- | |- | ||
− | | | + | |00:49 |
|Perpendicular bisector | |Perpendicular bisector | ||
|- | |- | ||
− | | | + | |00:51 |
|Definition of Transformation | |Definition of Transformation | ||
|- | |- | ||
− | | | + | |00:53 |
|Symmetrical transformation of a geometric figure is - | |Symmetrical transformation of a geometric figure is - | ||
|- | |- | ||
− | | | + | |00:57 |
|A change in its position, size or shape on a coordinate plane | |A change in its position, size or shape on a coordinate plane | ||
|- | |- | ||
− | | | + | |01:02 |
|Original figure is called 'Object' | |Original figure is called 'Object' | ||
|- | |- | ||
− | | | + | |01:04 |
|Transformed figure is called 'Image' | |Transformed figure is called 'Image' | ||
|- | |- | ||
− | | | + | |01:07 |
|Reflection symmetry | |Reflection symmetry | ||
|- | |- | ||
− | | | + | |01:09 |
|Is also called as Line symmetry | |Is also called as Line symmetry | ||
|- | |- | ||
− | | | + | |01:11 |
|A type of symmetry where one half is the reflection of the other half | |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 | |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. | |Line of Symmetry is the line over which the figure is reflected. | ||
|- | |- | ||
− | | | + | |01:24 |
|Let's Switch to GeoGebra window | |Let's Switch to GeoGebra window | ||
|- | |- | ||
− | | | + | |01:27 |
|Look on Dash home >>Media Apps>>Under Type >>Choose Education>> and Geogebra | |Look on Dash home >>Media Apps>>Under Type >>Choose Education>> and Geogebra | ||
|- | |- | ||
− | | | + | |01:37 |
|For this tutorial I am closing the Algebric view | |For this tutorial I am closing the Algebric view | ||
|- | |- | ||
− | | | + | |01:40 |
|Click on Close button on Algebric view | |Click on Close button on Algebric view | ||
|- | |- | ||
− | | | + | |01:47 |
|Let's start with “Line of symmetry” | |Let's start with “Line of symmetry” | ||
|- | |- | ||
− | | | + | |01:50 |
|First let's construct an equilateral triangle. | |First let's construct an equilateral triangle. | ||
|- | |- | ||
− | | | + | |01:53 |
|Select “Regular Polygon” tool from the toolbar. | |Select “Regular Polygon” tool from the toolbar. | ||
|- | |- | ||
− | | | + | |01:57 |
|Click on drawing pad points 'A' ,'B', and enter 3 for the number of sides. | |Click on drawing pad points 'A' ,'B', and enter 3 for the number of sides. | ||
|- | |- | ||
− | | | + | |02:08 |
|An equilateral triangle 'ABC' is drawn | |An equilateral triangle 'ABC' is drawn | ||
|- | |- | ||
− | | | + | |02:11 |
|Let's draw a perpendicular bisector to one of the sides of triangle | |Let's draw a perpendicular bisector to one of the sides of triangle | ||
|- | |- | ||
− | | | + | |02:15 |
|Select “Perpendicular Bisector Tool” and click on side AC | |Select “Perpendicular Bisector Tool” and click on side AC | ||
|- | |- | ||
− | | | + | |02:26 |
|Select the Point tool and create a point inside the triangle. | |Select the Point tool and create a point inside the triangle. | ||
|- | |- | ||
− | | | + | |02:31 |
|Move the point D towards one of the vertices . | |Move the point D towards one of the vertices . | ||
|- | |- | ||
− | | | + | |02:38 |
|Right click on point D and select Trace ON | |Right click on point D and select Trace ON | ||
|- | |- | ||
− | | | + | |02:43 |
|Select “Reflect Object about Line”tool from the tool bar | |Select “Reflect Object about Line”tool from the tool bar | ||
|- | |- | ||
− | | | + | |02:48 |
|Click on the point D | |Click on the point D | ||
|- | |- | ||
− | | | + | |02:49 |
|This will highlight Point D | |This will highlight Point D | ||
|- | |- | ||
− | | | + | |02:52 |
|Click on perpendicular Bisector | |Click on perpendicular Bisector | ||
|- | |- | ||
− | | | + | |02:55 |
|This will produce reflected image D' on the other side of perpendicular bisector | |This will produce reflected image D' on the other side of perpendicular bisector | ||
|- | |- | ||
− | | | + | |03:01 |
|'D is mirror image of point 'D' | |'D is mirror image of point 'D' | ||
|- | |- | ||
− | | | + | |03:04 |
|Set Trace On for the point D' | |Set Trace On for the point D' | ||
|- | |- | ||
− | | | + | |03:08 |
|Let us move the point D along the triangle using Move tool | |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 | |Click on the first option under Move tool from the toolbar | ||
|- | |- | ||
− | | | + | |03:22 |
|Click on figure with the mouse. | |Click on figure with the mouse. | ||
|- | |- | ||
− | | | + | |03:25 |
|Drag it tracing the triangle . | |Drag it tracing the triangle . | ||
|- | |- | ||
− | | | + | |03:28 |
|Now release the mouse button. | |Now release the mouse button. | ||
|- | |- | ||
− | | | + | |03:31 |
|What do you notice ? | |What do you notice ? | ||
|- | |- | ||
− | | | + | |03:32 |
|Here perpendicular bisector is the line of symmetry | |Here perpendicular bisector is the line of symmetry | ||
|- | |- | ||
− | | | + | |03:36 |
|D is the object and D' is the image | |D is the object and D' is the image | ||
|- | |- | ||
− | | | + | |03:39 |
|Let's reflect a semicircle about a line | |Let's reflect a semicircle about a line | ||
|- | |- | ||
− | | | + | |03:43 |
|Let's draw a semicircle | |Let's draw a semicircle | ||
|- | |- | ||
− | | | + | |03:44 |
|Click on the “Semicircle through Two points” tool Mark point E and then F | |Click on the “Semicircle through Two points” tool Mark point E and then F | ||
|- | |- | ||
− | | | + | |03:56 |
|Click on segment Between two Points | |Click on segment Between two Points | ||
|- | |- | ||
− | | | + | |04:02 |
|Mark points G and H A line is drawn | |Mark points G and H A line is drawn | ||
|- | |- | ||
− | | | + | |04:06 |
|Let's change the property of the line | |Let's change the property of the line | ||
Line 253: | Line 253: | ||
|- | |- | ||
− | | | + | |04:21 |
|Select “Reflect Object about Line” tool from the toolbar | |Select “Reflect Object about Line” tool from the toolbar | ||
|- | |- | ||
− | | | + | |04:27 |
|Click on the semicircle EF | |Click on the semicircle EF | ||
|- | |- | ||
− | | | + | |04:31 |
|Click on line GH | |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 | |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 | |Let us save this file now | ||
|- | |- | ||
− | | | + | |04:47 |
|Click on “File”>> "Save As" | |Click on “File”>> "Save As" | ||
|- | |- | ||
− | | | + | |04:50 |
|I will type the file name as "Line-symmetry" and click on “Save” | |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” | |Next, let us learn to “Rotate the Object around a Point by Angle” | ||
|- | |- | ||
− | | | + | |05:12 |
|Definition of Rotation | |Definition of Rotation | ||
|- | |- | ||
− | | | + | |05:15 |
|A rotation is a transformation that turns a figure around a fixed center by an angle | |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 | |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 | |You can rotate object at any degree measure Rotation can be clockwise and counterclockwise | ||
|- | |- | ||
− | | | + | |05:39 |
|Let's open a new Geogebra window | |Let's open a new Geogebra window | ||
|- | |- | ||
− | | | + | |05:41 |
|click on “File” >> New | |click on “File” >> New | ||
|- | |- | ||
− | | | + | |05:47 |
|Let us construct a square. | |Let us construct a square. | ||
|- | |- | ||
− | | | + | |05:49 |
|click on “Regular Polygon” tool from the toolbar | |click on “Regular Polygon” tool from the toolbar | ||
|- | |- | ||
− | | | + | |05:55 |
|Click on the drawing pad | |Click on the drawing pad | ||
|- | |- | ||
− | | | + | |05:57 |
|Mark points 'A' and 'B' | |Mark points 'A' and 'B' | ||
|- | |- | ||
− | | | + | |05:59 |
|A dialog box opens | |A dialog box opens | ||
|- | |- | ||
− | | | + | |06:01 |
|Click on OK | |Click on OK | ||
|- | |- | ||
− | | | + | |06:03 |
|A square 'ABCD' is drawn | |A square 'ABCD' is drawn | ||
|- | |- | ||
− | | | + | |06:05 |
|Click on “Rotate Object around a Point by Angle” tool | |Click on “Rotate Object around a Point by Angle” tool | ||
|- | |- | ||
− | | | + | |06:13 |
|Click on the Square 'ABCD' | |Click on the Square 'ABCD' | ||
|- | |- | ||
− | | | + | |06:16 |
|This will highlight the square | |This will highlight the square | ||
|- | |- | ||
− | | | + | |06:18 |
|Next Click on any one of the vertices | |Next Click on any one of the vertices | ||
|- | |- | ||
− | | | + | |06:20 |
|I will click on 'A' | |I will click on 'A' | ||
|- | |- | ||
− | | | + | |06:23 |
|A dialog box opens | |A dialog box opens | ||
|- | |- | ||
− | | | + | |06:25 |
|Type “60” in the Angle field | |Type “60” in the Angle field | ||
|- | |- | ||
− | | | + | |06:30 |
|Select "°" from first drop down list | |Select "°" from first drop down list | ||
|- | |- | ||
− | | | + | |06:35 |
|Select the option “clockwise” | |Select the option “clockwise” | ||
Click on OK | Click on OK | ||
|- | |- | ||
− | | | + | |06:40 |
|This will rotate the square clockwise at the point of selection with the angle of 60° | |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 | |The rotated image 'A`B`C` 'D' is formed | ||
|- | |- | ||
− | | | + | |06:49 |
|Let's move this figure aside using Move tool | |Let's move this figure aside using Move tool | ||
|- | |- | ||
− | | | + | |07:00 |
|Next, let's “Dilate or enlarge object from point by factor” | |Next, let's “Dilate or enlarge object from point by factor” | ||
|- | |- | ||
− | | | + | |07:09 |
|Dilation | |Dilation | ||
|- | |- | ||
− | | | + | |07:11 |
|Dilation or enlargement is a transformation | |Dilation or enlargement is a transformation | ||
|- | |- | ||
− | | | + | |07:14 |
|in which a figure is enlarged using a scale factor | |in which a figure is enlarged using a scale factor | ||
|- | |- | ||
− | | | + | |07:23 |
|Let's draw a triangle Using the “Polygon”tool | |Let's draw a triangle Using the “Polygon”tool | ||
|- | |- | ||
− | | | + | |07:28 |
|E , F , G click on E again to complete the triangle | |E , F , G click on E again to complete the triangle | ||
|- | |- | ||
− | | | + | |07:36 |
|Click on New point tool and | |Click on New point tool and | ||
|- | |- | ||
− | | | + | |07:40 |
|Mark a point 'H' | |Mark a point 'H' | ||
|- | |- | ||
− | | | + | |07:44 |
|Click on “Dilate Object from Point by Factor” tool | |Click on “Dilate Object from Point by Factor” tool | ||
|- | |- | ||
− | | | + | |07:51 |
|Click on the triangle 'EFG' | |Click on the triangle 'EFG' | ||
|- | |- | ||
− | | | + | |07:54 |
|This will highlight the triangle | |This will highlight the triangle | ||
|- | |- | ||
− | | | + | |07:55 |
|Click on the point 'H' | |Click on the point 'H' | ||
|- | |- | ||
− | | | + | |07:57 |
|A dialog box opens | |A dialog box opens | ||
|- | |- | ||
− | | | + | |08:00 |
|Type value of 2 in the number field | |Type value of 2 in the number field | ||
|- | |- | ||
− | | | + | |08:04 |
|Click on OK | |Click on OK | ||
|- | |- | ||
− | | | + | |08:09 |
|This will dilate or enlarge the object twice | |This will dilate or enlarge the object twice | ||
|- | |- | ||
− | | | + | |08:16 |
|Click on Segment Between two Points, join points H,E,E' | |Click on Segment Between two Points, join points H,E,E' | ||
|- | |- | ||
− | | | + | |08:33 |
|join points H,G,G' | |join points H,G,G' | ||
|- | |- | ||
− | | | + | |09:01 |
|join points H,F,F' | |join points H,F,F' | ||
|- | |- | ||
− | | | + | |09:15 |
|Here you can see that H is the point of dilation | |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 | |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 | |Let us save this file now | ||
|- | |- | ||
− | | | + | |09:30 |
|Click on “File”>> "Save As" | |Click on “File”>> "Save As" | ||
|- | |- | ||
− | | | + | |09:33 |
|I will type the file name as "Dilate-triangle" | |I will type the file name as "Dilate-triangle" | ||
|- | |- | ||
− | | | + | |09:48 |
|Click on “Save” with this we come to the end of this tutorial | |Click on “Save” with this we come to the end of this tutorial | ||
|- | |- | ||
− | | | + | |09:55 |
|Let's summarize | |Let's summarize | ||
Revision as of 12:08, 9 July 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 |
9:58 | 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