GeoGebra-5.04/C2/Types-of-Symmetry/English-timed
From Script | Spoken-Tutorial
Revision as of 11:23, 4 April 2022 by PoojaMoolya (Talk | contribs)
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. |
14:02 | The video at the following link summarises the Spoken Tutorial project.
Please download and watch it. |
14:10 | The Spoken Tutorial Project team, conducts workshops and gives certificates.
For more details, please write to us. |
14:20 | Please post your timed queries in this forum. |
14:24 | Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India. More information on this mission is available at this link. |
14:36 | This is Madhuri Ganapathi from, IIT Bombay signing off. Thank you for watching. |