https://script.spoken-tutorial.org/index.php?title=GeoGebra-5.04/C2/Types-of-Symmetry/English-timed&feed=atom&action=historyGeoGebra-5.04/C2/Types-of-Symmetry/English-timed - Revision history2024-03-29T10:06:46ZRevision history for this page on the wikiMediaWiki 1.23.17https://script.spoken-tutorial.org/index.php?title=GeoGebra-5.04/C2/Types-of-Symmetry/English-timed&diff=55900&oldid=prevPoojaMoolya at 05:53, 4 April 20222022-04-04T05:53:14Z<p></p>
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</table>PoojaMoolyahttps://script.spoken-tutorial.org/index.php?title=GeoGebra-5.04/C2/Types-of-Symmetry/English-timed&diff=49374&oldid=prevPoojaMoolya: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- |00:01 | Welcome to this tutorial on '''Types of Symmetry''' in '''GeoGebra'''. |- |00:06 |In this tutorial we will learn abou..."2019-10-10T09:37:22Z<p>Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- |00:01 | Welcome to this tutorial on '''Types of Symmetry''' in '''GeoGebra'''. |- |00:06 |In this tutorial we will learn abou..."</p>
<p><b>New page</b></p><div>{|border=1<br />
||'''Time'''<br />
||'''Narration'''<br />
<br />
|-<br />
|00:01<br />
| Welcome to this tutorial on '''Types of Symmetry''' in '''GeoGebra'''. <br />
<br />
|- <br />
|00:06<br />
|In this tutorial we will learn about various types of symmetry like: <br />
<br />
Line <br />
<br />
Point <br />
<br />
|- <br />
|00:15<br />
| Rotation <br />
<br />
Translational <br />
<br />
Scale <br />
<br />
|- <br />
|00:22<br />
| To record this tutorial, I am using, <br />
<br />
'''Ubuntu Linux''' OS version 14.04 <br />
<br />
'''GeoGebra''' version 5.0.438.0-d. <br />
<br />
|- <br />
|00:36<br />
| To follow this tutorial, you should be familiar with, the '''Geogebra''' interface. <br />
<br />
If not, for relevant '''GeoGebra''' tutorials please visit our website. <br />
<br />
|- <br />
| 00:49<br />
| Let us begin with the definition of symmetry. <br />
<br />
|- <br />
|00:53<br />
| 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. <br />
<br />
|- <br />
|01:08<br />
|I have already opened the '''GeoGebra''' interface. <br />
<br />
|- <br />
|01:12<br />
| For this tutorial I will uncheck the axes. <br />
<br />
|- <br />
|01:16<br />
| To do so, right-click on the '''Graphics''' view. <br />
The '''Graphics''' menu appears. <br />
<br />
|- <br />
|01:23<br />
|In this menu, uncheck the '''Axes''' check box. <br />
<br />
|- <br />
|01:27<br />
| For this tutorial, we will use all the tools available under the '''Reflect about Line''' tool. <br />
<br />
|- <br />
|01:35<br />
| Now we will define line symmetry.<br />
<br />
|- <br />
|01:38<br />
| A figure has line symmetry, if one half of the object is the mirror image of the other half. <br />
<br />
|- <br />
|01:46<br />
| The line over which the figure is reflected is called the line of symmetry.<br />
<br />
|- <br />
|01:52<br />
| To draw a vertical line '''AB''', click on the '''Segment''' tool and then click on '''Graphics view'''. <br />
<br />
|- <br />
|02:00<br />
| Point '''A''' is drawn in the '''Graphics view'''. <br />
<br />
|- <br />
|02:04<br />
| Click again directly below point '''A''' to draw segment '''AB'''. <br />
Note that it is labelled as '''f'''. <br />
<br />
|- <br />
|02:13<br />
| Select the '''Semicircle through 2 Points''' tool. <br />
<br />
|- <br />
|02:17<br />
| Click on the left-side of segment '''AB'''. Point '''C''' is drawn. <br />
<br />
|- <br />
|02:24<br />
| A gain click below '''C''' to complete the semicircle '''CD''' named as '''c.''' <br />
<br />
|- <br />
|02:30<br />
| This semicircle should be to the left of segment '''f'''. <br />
<br />
|- <br />
|02:35<br />
| Now let us reflect the semicircle about the segment '''f'''.<br />
<br />
|- <br />
|02:40<br />
| Click on the '''Reflect about Line''' tool. Click on the semicircle, then click on line '''f'''. <br />
<br />
|- <br />
|02:50<br />
| Semicircle '''c''''(c prime) appears on the right side of segment '''f'''. It is a reflected image of semicircle '''c'''. <br />
<br />
|- <br />
|03:00<br />
|Let's change the object properties of '''c''' and '''c''''(c prime).<br />
<br />
|- <br />
|03:05<br />
| Right-click on '''c''' and select '''Object Properties'''. <br />
<br />
|- <br />
|03:11<br />
| '''Preferences''' window opens. <br />
<br />
|- <br />
|03:14<br />
| In the left panel under '''Conic''', '''c''' is already selected. <br />
<br />
|- <br />
|03:19<br />
| While holding the '''Ctrl''' key, click on '''c''''(c prime). <br />
<br />
|- <br />
|03:23<br />
| In the '''Basic''' tab, click the '''Show Trace''' check box. <br />
<br />
|- <br />
|03:28<br />
| In the '''Color '''tab, I will choose the colour as pink. <br />
<br />
|- <br />
|03:33<br />
| You may choose any colour of your choice. Then close the '''Preferences''' window. <br />
<br />
|- <br />
|03:40<br />
| Using the '''Move''' tool, drag the semicircle '''c''' .<br />
<br />
|- <br />
|03:46<br />
|Observe that semicircle '''c''''(c prime) moves as we move ''' c'''. <br />
<br />
|- <br />
|03:52<br />
| '''c''''(c prime) is the mirror image of '''c''', with segment '''f''' as the mirror. <br />
<br />
|- <br />
|03:58<br />
| To erase the traces, drag the '''Graphics view'''. <br />
<br />
|- <br />
|04:03<br />
|Let us delete all the objects in the '''Graphics view'''. <br />
<br />
|- <br />
|04:07<br />
| Press '''Ctrl + A ''' keys to select all the objects. <br />
<br />
|- <br />
|04:11<br />
| Then press the '''Delete''' key on the keyboard. <br />
<br />
|- <br />
|04:15<br />
| Now let us learn to reflect about a point. <br />
<br />
|- <br />
|04:19<br />
| Click on '''Segment ''' tool. <br />
<br />
|- <br />
|04:22<br />
| Click within the '''Graphics view''' twice to draw a segment '''AB'''. <br />
<br />
|- <br />
|04:28<br />
| Select the '''Reflect about Point''' tool. Click on point '''A''', then on point '''B'''. <br />
<br />
|- <br />
|04:38<br />
| '''A''''(A prime)which is the reflected image of '''A''', appears on the otherside of point '''B'''. <br />
<br />
|- <br />
| 04:45<br />
|To view '''A' '''(A prime), drag the '''Graphics view''' if required. <br />
<br />
|- <br />
|04:50<br />
|To show that '''A''''(A prime) is the image of '''A''', we will measure the distances '''AB''' and '''A''''(A prime)'''B'''. <br />
<br />
|- <br />
|04:58<br />
|Under '''Angle''', click on the '''Distance or Length''' tool. <br />
<br />
|- <br />
|05:03<br />
|Click on point '''A''', then on '''B'''. <br />
<br />
|- <br />
|05:08<br />
|Again click on '''A'''' (A prime) and then on '''B'''. <br />
<br />
|- <br />
|05:15<br />
| Notice that the distances '''AB''' and '''A''''(A prime)'''B ''' are equal. <br />
<br />
|- <br />
|05:20<br />
| Using '''Move''' tool, I will drag segment '''AB''' upwards. <br />
<br />
|- <br />
|05:27<br />
| Observe that '''A''''(A prime) also moves along with '''AB'''. <br />
<br />
|- <br />
|05:32<br />
| Now we will learn to reflect a point about a circle. <br />
<br />
|- <br />
|05:36<br />
| Select the''' Circle with centre and radius '''tool. Click within the '''Graphics view'''. <br />
<br />
|- <br />
|05:43<br />
| The '''Circle with Centre and Radius''' text box appears. <br />
<br />
|- <br />
|05:48<br />
| In the text box type ''' Radius''' as 2 and click on the '''OK''' button at the bottom. <br />
<br />
|- <br />
|05:56<br />
| A circle with centre '''C''' and radius 2 cm is drawn in the '''Graphics view'''. <br />
<br />
|- <br />
|06:02<br />
| Using '''Point''' tool, draw a point '''D''' outside the circle. <br />
<br />
|- <br />
|06:09<br />
|Select the''' Reflect about Circle''' tool. Click on point '''D''' and then click on circle '''c'''. <br />
<br />
|- <br />
|06:19<br />
| '''D''''(D prime), which is the image of '''D''', appears inside the circle. <br />
<br />
|- <br />
|06:24<br />
| Click on the '''Move''' tool and drag point '''D''' around the circle. <br />
<br />
|- <br />
|06:31<br />
|Observe that '''D''''(D prime) also moves inside the circle mirroring '''D'''. <br />
<br />
|- <br />
|06:37<br />
| Drag point '''D''' inside the circle and see what happens. '''D''' and '''D''''(D prime)exchange places. <br />
<br />
|- <br />
|06:47<br />
| Now let us learn about rotational symmetry. <br />
<br />
|- <br />
|06:51<br />
| An object has rotational symmetry, if it can be rotated about a fixed point without changing the overall shape. <br />
<br />
|- <br />
| 07:02<br />
| Let us open a new '''GeoGebra''' window. <br />
<br />
|- <br />
|07:06<br />
| Click on ''' File ''' and then on '''New Window'''. <br />
<br />
|- <br />
|07:11<br />
| We will now rotate an object around a point. For this, I will draw a square. <br />
<br />
|- <br />
|07:18<br />
| Click on the '''Polygon''' tool. <br />
<br />
|- <br />
|07:21<br />
| Click within the '''Graphics view''' to draw point '''A'''. Similarly draw points '''B''', '''C''' and '''D'''. <br />
<br />
|- <br />
|07:33<br />
| To complete the polygon click again on point '''A'''. <br />
<br />
|- <br />
|07:37<br />
| A quadrilateral '''ABCD''' named as '''q1''' is drawn. <br />
<br />
|- <br />
|07:42<br />
| To convert '''q1''' to a square, we have to adjust the lengths. <br />
<br />
|- <br />
|07:47<br />
| Click on the '''Move''' tool and drag the points '''A''', '''B''', '''C''' and '''D'''. <br />
<br />
|- <br />
|07:54<br />
| Notice the change in the lengths in the '''Algebra view'''. All the lengths have to be same. <br />
<br />
|- <br />
|08:01<br />
| We will now draw perpendicular bisectors to the square. <br />
<br />
|- <br />
|08:05<br />
| Click on '''Perpendicular Bisector''' tool. <br />
<br />
|- <br />
|08:08<br />
| Click on points '''A''', '''B''' and '''B''', '''C'''. <br />
<br />
|- <br />
|08:14<br />
| The two perpendicular bisectors intersect at a point. <br />
<br />
|- <br />
|08:18<br />
| Click on '''Intersect''' tool and click on point of intersection. Point '''E ''' is the point of intersection. <br />
<br />
|- <br />
|08:28<br />
| Let us create an angle slider. Click on '''Slider''' tool and click in the '''Graphics view.''' <br />
<br />
|- <br />
|08:37<br />
| The '''Slider '''dialog box appears. <br />
<br />
|- <br />
|08:40<br />
| Select '''Angle''' radio button. <br />
<br />
|- <br />
|08:43<br />
| '''Alpha''' appears in the '''Name field'''. <br />
<br />
|- <br />
|08:47<br />
| Leave the default values of '''Min''', '''Max ''' and '''Increment''' as they are. <br />
<br />
And click on the '''OK''' button at the bottom. <br />
<br />
|- <br />
|08:58<br />
| Alpha slider is created in the '''Graphics view'''. <br />
<br />
|- <br />
|09:02<br />
| Now click on the '''Rotate around Point''' tool. Click on the square '''q1''' and then point '''E'''. <br />
<br />
|- <br />
|09:12<br />
| '''Rotate around Point''' text box appears with 45 degrees angle. <br />
<br />
|- <br />
|09:18<br />
| Below the text box we have, '''counter clockwise''' and '''clockwise''' radio buttons. <br />
<br />
|- <br />
|09:25<br />
| You can select any one of the radio buttons as per your choice. <br />
<br />
I will select '''clockwise'''. <br />
<br />
|- <br />
|09:33<br />
| Delete 45 degrees from the '''Angle''' text box. <br />
<br />
|- <br />
|09:37<br />
| In the '''Angle''' text box, notice an alpha symbol on the rightside. <br />
<br />
|- <br />
|09:43<br />
| Click on it to show the table of symbols. <br />
<br />
|- <br />
|09:47<br />
| Select '''alpha''' from the table and click on the '''OK''' button at the bottom. <br />
<br />
|- <br />
|09:54<br />
|Observe that a new square '''q1'''' appears in the '''Graphics view'''. <br />
<br />
|- <br />
|10:00<br />
| This square '''q1' ''' is rotated at angle alpha with respect to square '''q1'''. <br />
<br />
|- <br />
|10:07<br />
| Now drag the '''alpha''' slider between 0 degrees to 360 degrees. <br />
<br />
|- <br />
|10:13<br />
| As we drag, notice the rotation of '''q1'''' around the point '''E'''. <br />
<br />
|- <br />
|10:20<br />
| As an assignment, <br />
<br />
Draw a hexagon and show its rotation symmetry. <br />
<br />
|-<br />
|10:28<br />
| Let us now delete all the objects. <br />
<br />
|- <br />
|10:31<br />
| Go to '''Edit''' menu and navigate to '''Select All'''. <br />
Then select the '''Delete''' option. <br />
<br />
|- <br />
| 10:41<br />
| Next we will move an object using a vector. <br />
<br />
|- <br />
|10:45<br />
|Let us define translational symmetry <br />
<br />
|- <br />
|10:49<br />
| An object has '''translational''' symmetry if, it can be moved without changing its overall shape. <br />
<br />
|- <br />
|10:58<br />
| Using the '''Polygon''' tool draw a triangle '''ABC''' named as '''t1'''. <br />
<br />
|- <br />
|11:08<br />
| To draw a vector, click on the''' Vector''' tool from the tool bar. <br />
<br />
|- <br />
|11:13<br />
| Click on point '''D''' and then on point '''E'''. <br />
<br />
|- <br />
|11:19<br />
| The vector is represented by''' u.''' <br />
<br />
|- <br />
|11:23<br />
| Select '''Translate by Vector ''' tool. Click on the triangle '''t1''' and then on the vector '''u'''. <br />
<br />
|- <br />
|11:33<br />
| Here '''t1' ''' is the translated image of '''t1'''. <br />
<br />
|- <br />
|11:38<br />
| The distance between '''t1''' and '''t1' '''is exactly same as the length of vector '''u'''. <br />
<br />
|- <br />
|11:45<br />
|Using the '''Move''' tool, drag point '''E''' of the vector '''u'''. <br />
<br />
Observe that the image triangle '''t1'''' translates along with vector '''u'''. <br />
<br />
|- <br />
|11:59<br />
| As an assignment, <br />
<br />
Draw a vector.<br />
<br />
|- <br />
|12:04<br />
| Translate a point using '''Translate by Vector''' tool.<br />
<br />
|- <br />
|12:08<br />
| Measure the distance between the original point and the translated point. <br />
<br />
|- <br />
|12:13<br />
| Let us define scale symmetry. <br />
<br />
|- <br />
|12:16<br />
| An object has '''scale''' symmetry if, it does not change shape when it is expanded or contracted. <br />
<br />
|- <br />
|12:25<br />
| Let us open a new Geogebra window. Click on '''File''' and select '''New Window'''. <br />
<br />
|- <br />
|12:34<br />
| Now let us learn how to dilate an object.<br />
<br />
|- <br />
|12:38<br />
| Click on the '''Circle with centre and radius '''tool. Then click on the '''Graphics view'''. <br />
<br />
|- <br />
|12:45<br />
| Type radius as 1 in the '''Circle with Centre and Radius''' text box. <br />
<br />
|- <br />
|12:50<br />
| Click on '''OK ''' button at the bottom. <br />
<br />
|- <br />
|12:53<br />
| Using '''Point''' tool draw a point '''B''' outside the circle. <br />
<br />
|- <br />
|12:59<br />
| Select the '''Dilate from Point''' tool. <br />
<br />
|- <br />
|13:02<br />
| Click on the circumference of the unit circle then click on point '''B'''. <br />
<br />
|- <br />
|13:09<br />
| The '''Dilate from Point''' text box appears. Type the '''Factor''' as 2 and click on the '''OK''' button at the bottom. <br />
<br />
|- <br />
|13:20<br />
| A dilated circle with double the radius appears in the '''Graphics view'''. <br />
<br />
|- <br />
|13:26<br />
| As an assignment,<br />
<br />
Draw a pentagon and a hexagon on the same window. <br />
<br />
|- <br />
|13:32<br />
| Dilate the pentagon by a factor of 0.5 <br />
<br />
Dilate the hexagon by a factor of 3. <br />
<br />
|- <br />
|13:40<br />
| Let us summarise what we have learnt. <br />
<br />
|- <br />
|13:44<br />
| In this tutorial we have learnt about <br />
<br />
Symmetry and various types of symmetry <br />
<br />
Line <br />
<br />
Point <br />
<br />
|- <br />
|12:56<br />
|Rotation <br />
<br />
Translational <br />
<br />
Scale. <br />
<br />
|- <br />
|14:02<br />
| The video at the following link summarises the Spoken Tutorial project. <br />
Please download and watch it. <br />
<br />
|- <br />
|14:10<br />
| The '''Spoken Tutorial Project '''team, conducts workshops and gives certificates. <br />
<br />
For more details, please write to us. <br />
<br />
|- <br />
|14:20<br />
| Please post your timed queries in this forum. <br />
<br />
|- <br />
|14:24<br />
| Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India. More information on this mission is available at this link. <br />
<br />
|- <br />
| 14:36<br />
|This is Madhuri Ganapathi from, IIT Bombay signing off. Thank you for watching. <br />
|-<br />
|}</div>PoojaMoolya