Difference between revisions of "Geogebra/C3/Theorems-on-Chords-and-Arcs/English-timed"
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||you will be able to verify theorems on | ||you will be able to verify theorems on | ||
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+ | ||Chords of circle. | ||
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+ | || Arcs of circle. | ||
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+ | ||00:18 | ||
||We assume that you have the basic working knowledge of Geogebra. | ||We assume that you have the basic working knowledge of Geogebra. | ||
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||00:23 | ||00:23 | ||
− | ||If not,For relevant tutorials, please visit our website http://spoken-tutorial.org | + | ||If not, For relevant tutorials, please visit our website: http://spoken-tutorial.org |
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|| 00:30 | || 00:30 | ||
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− | ||Ubuntu Linux OS Version 11.10 Geogebra Version 3.2.47.0 | + | ||Ubuntu Linux OS Version 11.10 |
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+ | ||00:36 | ||
+ | ||Geogebra Version 3.2.47.0 | ||
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||We will use the following Geogebra tools | ||We will use the following Geogebra tools | ||
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||* Circular Sector with Center between Two Points | ||* Circular Sector with Center between Two Points | ||
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||* Midpoint and | ||* Midpoint and | ||
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+ | ||00:58 | ||
+ | ||Perpendicular line | ||
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||01:00 | ||01:00 | ||
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||01:02 | ||01:02 | ||
− | ||Click on Dash home Media Apps. | + | ||Click on Dash home, Media Apps. |
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||Under Type Choose Education and GeoGebra. | ||Under Type Choose Education and GeoGebra. | ||
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||Let's state a theorem | ||Let's state a theorem | ||
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|| '''Perpendicular from center of circle to a chord bisects the chord''' | || '''Perpendicular from center of circle to a chord bisects the chord''' | ||
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||01:23 | ||01:23 | ||
− | ||'''Perpendicular from center A of a circle to chord BC bisects it''' | + | ||'''Perpendicular from the center A of a circle to chord BC bisects it''' |
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||01:44 | ||01:44 | ||
− | ||In the 'Graphic view' | + | ||In the ''' 'Graphic view' ''' uncheck ''' 'Axes' ''' |
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||Select 'Grid' | ||Select 'Grid' | ||
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||Let's draw a circle. | ||Let's draw a circle. | ||
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||02:01 | ||02:01 | ||
− | ||A dialogue box | + | ||A dialogue box opens |
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||02:03 | ||02:03 | ||
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||Let's Move the point 'A' and see the movement of the circle. | ||Let's Move the point 'A' and see the movement of the circle. | ||
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||Click on "Perpendicular line" tool from tool bar | ||Click on "Perpendicular line" tool from tool bar | ||
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||Click on the chord 'BC', and point 'A'. | ||Click on the chord 'BC', and point 'A'. | ||
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||Let's Move the point 'B', and see how the perpendicular line moves along with point 'B'. | ||Let's Move the point 'B', and see how the perpendicular line moves along with point 'B'. | ||
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||Perpendicular line and Chord 'BC' intersect at a point | ||Perpendicular line and Chord 'BC' intersect at a point | ||
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||Click on “Intersect Two objects” tool, | ||Click on “Intersect Two objects” tool, | ||
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||Mark the point of intersection as 'D'. | ||Mark the point of intersection as 'D'. | ||
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||Let's verify whether D is the mid point of chord BC | ||Let's verify whether D is the mid point of chord BC | ||
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− | ||Click on the "Distance" tool | + | ||Click on the "Distance" tool. |
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||Click on the points ,'B' 'D' ...'D' 'C' ... | ||Click on the points ,'B' 'D' ...'D' 'C' ... | ||
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||Click on the points 'C','D', 'A' | ||Click on the points 'C','D', 'A' | ||
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||03:42 | ||03:42 | ||
− | || angle 'CDA' is '90 | + | || angle 'CDA' is '90 degrees |
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||03:46 | ||03:46 | ||
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||03:50 | ||03:50 | ||
− | ||Let's Move the point 'C' | + | ||Let's Move the point 'C' and see how the distances move along with point 'C' |
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||04:03 | ||04:03 | ||
||Let us save the file now | ||Let us save the file now | ||
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||04:05 | ||04:05 | ||
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||04:08 | ||04:08 | ||
− | ||I will type the file name as "circle-chord" | + | ||I will type the file name as "circle-chord" |
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+ | ||04:12 | ||
+ | ||circle-chord | ||
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+ | ||04:16 | ||
+ | || Click on Save | ||
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||04:21 | ||04:21 | ||
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||Let's verify the theorem. | ||Let's verify the theorem. | ||
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||Let'sOpen a new Geogebra window, | ||Let'sOpen a new Geogebra window, | ||
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||04:57 | ||04:57 | ||
− | ||Click on " the Circle with Center through | + | ||Click on "' the Circle with Center through Point''' tool from toolbar |
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||05:04 | ||05:04 | ||
− | || and click again to get point 'B' | + | || and click again to get point 'B' |
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||Let's draw an arc 'BC' | ||Let's draw an arc 'BC' | ||
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||05:13 | ||05:13 | ||
− | ||Click on "Circular Arc with Center between Two points" | + | ||Click on "'Circular Arc with Center between Two points"' |
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− | ||Click on the point 'A'B' and 'C' on the circumference | + | ||Click on the point 'A', 'B' and 'C' on the circumference |
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||05:24 | ||05:24 | ||
||An Arc 'BC' is drawn | ||An Arc 'BC' is drawn | ||
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||Let's change the properties of arc 'BC' | ||Let's change the properties of arc 'BC' | ||
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− | ||Select '' color'' as ''green'' click on | + | ||Select '' color'' as ''green'', click on '''Close.''' |
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||05:46 | ||05:46 | ||
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||05:56 | ||05:56 | ||
− | ||let's subtend two angles from arc BC to points 'D' | + | ||let's subtend two angles from arc BC to points 'D' and 'E'. |
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||Click on "Polygon" tool, | ||Click on "Polygon" tool, | ||
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||Click on the "Angle" tool, | ||Click on the "Angle" tool, | ||
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||Click on points 'B', 'D', 'C' and 'B', 'E', 'C' | ||Click on points 'B', 'D', 'C' and 'B', 'E', 'C' | ||
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||We can see that the angles 'BDC' and 'BEC' are equal. | ||We can see that the angles 'BDC' and 'BEC' are equal. | ||
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||Let's state a next theorem | ||Let's state a next theorem | ||
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||07:30 | ||07:30 | ||
− | ||Click on the | + | ||Click on the '"Circular Sector with Center between Two Points"' tool. |
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||08:45 | ||08:45 | ||
− | ||With this we come to the end of | + | ||With this we come to the end of this tutorial |
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||08:48 | ||08:48 | ||
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||Select Segment with Given length from point tool | ||Select Segment with Given length from point tool | ||
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||09:44 | ||09:44 | ||
− | ||Assignment | + | ||Assignment output should look like this |
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||09:48 | ||09:48 | ||
− | ||Watch the video available at this url http://spoken-tutorial.org/What is a Spoken Tutorial | + | ||Watch the video available at this url: http://spoken-tutorial.org/What is a Spoken Tutorial |
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||For more details, please write to contact@spoken-tutorial.org | ||For more details, please write to contact@spoken-tutorial.org | ||
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||10:25 | ||10:25 | ||
− | ||More information on this Mission is available at | + | ||More information on this Mission is available at this link |
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||10:29 | ||10:29 | ||
||This is Madhuri Ganapathi from IIT Bombay signing off .Thank you for joining | ||This is Madhuri Ganapathi from IIT Bombay signing off .Thank you for joining |
Revision as of 13:19, 8 August 2014
Time | Narration |
00:01 | Hello,Welcome to this tutorial on Theorems on Chords and Arcs in Geogebra |
00:08 | At the end of this tutorial, |
00:09 | you will be able to verify theorems on |
00:14 | Chords of circle. |
00:16 | Arcs of circle. |
00:18 | We assume that you have the basic working knowledge of Geogebra. |
00:23 | If not, For relevant tutorials, please visit our website: http://spoken-tutorial.org |
00:30 | To record this tutorial I am using |
00:32 | Ubuntu Linux OS Version 11.10 |
00:36 | Geogebra Version 3.2.47.0 |
00:42 | We will use the following Geogebra tools |
00:47 | * Circle with Center and Radius |
00:49 | * Circular Sector with Center between Two Points |
00:53 | * Circular Arc with Center between Two points |
00:56 | * Midpoint and |
00:58 | Perpendicular line |
01:00 | Let's open a new GeoGebra window. |
01:02 | Click on Dash home, Media Apps. |
01:06 | Under Type Choose Education and GeoGebra. |
01:15 | Let's state a theorem |
01:17 | Perpendicular from center of circle to a chord bisects the chord |
01:23 | Perpendicular from the center A of a circle to chord BC bisects it |
01:32 | Let's verify a theorem. |
01:37 | For this tutorial I will use 'Grid layout' instead of Axes |
01:42 | Right Click on the drawing pad |
01:44 | In the 'Graphic view' uncheck 'Axes' |
01:47 | Select 'Grid' |
01:51 | Let's draw a circle. |
01:54 | Select the "Circle with Center and Radius" tool from tool bar. |
01:58 | Mark a point 'A' on the drawing pad. |
02:01 | A dialogue box opens |
02:03 | Let's type value '3' for radius |
02:06 | Click OK. |
02:07 | A Circle with center 'A' and radius '3cm' is drawn |
02:13 | Let's Move the point 'A' and see the movement of the circle. |
02:19 | Select “Segment between two points” tool. |
02:22 | Mark points 'B' and 'C' on the circumference of the circle |
02:27 | A chord 'BC' is drawn. |
02:30 | Let's draw a perpendicular line to Chord 'BC' which passes through point 'A'. |
02:35 | Click on "Perpendicular line" tool from tool bar |
02:39 | Click on the chord 'BC', and point 'A'. |
02:44 | Let's Move the point 'B', and see how the perpendicular line moves along with point 'B'. |
02:52 | Perpendicular line and Chord 'BC' intersect at a point |
02:56 | Click on “Intersect Two objects” tool, |
02:58 | Mark the point of intersection as 'D'. |
03:03 | Let's verify whether D is the mid point of chord BC |
03:08 | Click on the "Distance" tool. |
03:11 | Click on the points ,'B' 'D' ...'D' 'C' ... |
03:19 | Notice that distances 'BD' and 'DC' are equal. |
03:24 | It implies 'D' is midpoint of chord 'BC' |
03:29 | Let's measure the angle 'CDA' |
03:33 | Click on Angle tool ... |
03:35 | Click on the points 'C','D', 'A' |
03:42 | angle 'CDA' is '90 degrees |
03:46 | TheTheorem is verified. |
03:50 | Let's Move the point 'C' and see how the distances move along with point 'C'
|
04:03 | Let us save the file now |
04:05 | Click on “File”>> "Save As" |
04:08 | I will type the file name as "circle-chord" |
04:12 | circle-chord |
04:16 | Click on Save |
04:21 | Let us move on to the next theorem. |
04:28 | Inscribed angles subtended by the same arc are equal. |
04:34 | Inscribed angles BDC and BEC subtended by the same arc BC are equal |
04:44 | Let's verify the theorem. |
04:48 | Let'sOpen a new Geogebra window, |
04:51 | Click on “File” >> "New" |
04:55 | Let's draw a circle |
04:57 | Click on "' the Circle with Center through Point tool from toolbar |
05:01 | Mark a point A' as centre |
05:04 | and click again to get point 'B' |
05:10 | Let's draw an arc 'BC' |
05:13 | Click on "'Circular Arc with Center between Two points"' |
05:17 | Click on the point 'A', 'B' and 'C' on the circumference |
05:24 | An Arc 'BC' is drawn |
05:26 | Let's change the properties of arc 'BC' |
05:30 | In the "Algebra View" |
05:32 | Right click on the object 'd' |
05:35 | Select "Object Properties" |
05:37 | Select color as green, click on Close. |
05:46 | Click on new point tool, mark points 'D' and 'E' on the circumference of the circle. |
05:56 | let's subtend two angles from arc BC to points 'D' and 'E'. |
06:03 | Click on "Polygon" tool, |
06:05 | click on the points 'E', 'B', 'D', 'C' and 'E' again to complete the figure. |
06:18 | Let's measure the angles 'BDC' and 'BEC' |
06:26 | Click on the "Angle" tool, |
06:28 | Click on points 'B', 'D', 'C' and 'B', 'E', 'C' |
06:40 | We can see that the angles 'BDC' and 'BEC' are equal. |
06:51 | Let's state a next theorem |
06:55 | Angle subtended by an arc at the center, is twice the inscribed angles subtended by the same arc |
07:06 | Angle BAC subtended by arc BC at A is twice the inscribed angles BEC and BDC subtended by the same arc |
07:22 | Let's verify the theorem |
07:26 | Let's draw a sector 'ABC' |
07:30 | Click on the '"Circular Sector with Center between Two Points"' tool. |
07:35 | click on the points 'A', 'B', 'C' |
07:45 | Let's change the color of sector 'ABC'. |
07:48 | Right click on sector 'ABC' |
07:51 | Select "Object Properties". |
07:54 | Select Color as “Green”. Click on "Close". |
08:00 | Let's the measure angle 'BAC' |
08:04 | Click on the "Angle" tool , Click on the points 'B', 'A', 'C' |
08:15 | Angle 'BAC' is twice the angles 'BEC' and 'BDC' |
08:28 | Let's move the point 'C' |
08:32 | Notice that angle 'BAC' is always twice the angles 'BEC' and 'BDC' |
08:41 | hence theorems are verified |
08:45 | With this we come to the end of this tutorial |
08:48 | let's summarize |
08:53 | In this tutorial, we have learnt to verify that: |
08:57 | * Perpendicular from center to a chord bisects it |
09:00 | * Inscribed angles subtended by the same arc are equal |
09:06 | * the Central angle of a circle is twice any inscribed angle subtended by the same arc |
09:15 | As an assignment I would like you to verify |
09:19 | Equal chords of a circle are equidistant from center. |
09:24 | Draw a circle. |
09:25 | Select Segment with Given length from point tool |
09:29 | Use it to draw two chords of equal size. |
09:33 | Draw perpendicular lines from center to chords. |
09:37 | Mark points of intersection. |
09:40 | Measure perpendicular distances. |
09:44 | Assignment output should look like this |
09:48 | Watch the video available at this url: http://spoken-tutorial.org/What is a Spoken Tutorial |
09:51 | It summarises the Spoken Tutorial project |
09:53 | If you do not have good bandwidth, you can download and watch it |
09:58 | The Spoken Tutorial Project Team : |
10:00 | Conducts workshops using spoken tutorials |
10:03 | Gives certificates to those who pass an online test |
10:06 | For more details, please write to contact@spoken-tutorial.org |
10:14 | Spoken Tutorial Project is a part of the Talk to a Teacher project |
10:18 | It is supported by the National Mission on Education through ICT, MHRD, Government of India |
10:25 | More information on this Mission is available at this link |
10:29 | This is Madhuri Ganapathi from IIT Bombay signing off .Thank you for joining |