Difference between revisions of "Geogebra/C3/Theorems-on-Chords-and-Arcs/English-timed"
From Script | Spoken-Tutorial
PoojaMoolya (Talk | contribs) |
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||01:06 | ||01:06 | ||
||Under Type Choose Education and GeoGebra. | ||Under Type Choose Education and GeoGebra. | ||
+ | |||
|- | |- | ||
||01:15 | ||01:15 | ||
||Let's state a theorem | ||Let's state a theorem | ||
+ | |||
|- | |- | ||
|| 01:17 | || 01:17 | ||
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||01:32 | ||01:32 | ||
||Let's verify a theorem. | ||Let's verify a theorem. | ||
+ | |||
|- | |- | ||
||01:37 | ||01:37 | ||
− | ||For this tutorial I will use 'Grid layout' instead of Axes | + | ||For this tutorial I will use '''Grid layout''' instead of Axes |
|- | |- | ||
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|- | |- | ||
||01:44 | ||01:44 | ||
− | ||In the | + | ||In the '''Graphic view''' uncheck '''Axes''' |
|- | |- | ||
||01:47 | ||01:47 | ||
− | ||Select 'Grid' | + | ||Select '''Grid''' |
|- | |- | ||
||01:51 | ||01:51 | ||
Line 108: | Line 111: | ||
|- | |- | ||
||01:54 | ||01:54 | ||
− | ||Select the | + | ||Select the '''Circle with Center and Radius''' tool from tool bar. |
|- | |- | ||
||01:58 | ||01:58 | ||
− | ||Mark a point 'A' on the drawing pad. | + | ||Mark a point '''A''' on the drawing pad. |
|- | |- | ||
||02:01 | ||02:01 | ||
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|- | |- | ||
||02:03 | ||02:03 | ||
− | ||Let's type value '3' for radius | + | ||Let's type value '''3''' for radius |
|- | |- | ||
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|- | |- | ||
||02:07 | ||02:07 | ||
− | ||A Circle with center 'A' and radius '3cm' is drawn | + | ||A Circle with center '''A''' and radius '''3cm''' is drawn |
|- | |- | ||
||02:13 | ||02:13 | ||
− | ||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. |
|- | |- | ||
||02:19 | ||02:19 | ||
− | ||Select | + | ||Select '''Segment between two points''' tool. |
|- | |- | ||
||02:22 | ||02:22 | ||
− | ||Mark points 'B' and 'C' on the circumference of the circle | + | ||Mark points '''B''' and '''C''' on the circumference of the circle |
|- | |- | ||
||02:27 | ||02:27 | ||
− | ||A chord 'BC' is drawn. | + | ||A chord '''BC''' is drawn. |
+ | |||
|- | |- | ||
||02:30 | ||02:30 | ||
− | ||Let's draw a perpendicular line to Chord 'BC' which passes through point 'A' | + | ||Let's draw a perpendicular line to Chord '''BC''' which passes through point '''A''' |
|- | |- | ||
||02:35 | ||02:35 | ||
− | ||Click on | + | ||Click on '''Perpendicular line''' tool from tool bar |
|- | |- | ||
||02:39 | ||02:39 | ||
− | ||Click on the chord 'BC', and point 'A'. | + | ||Click on the chord '''BC''', and point '''A'''. |
+ | |||
|- | |- | ||
||02:44 | ||02:44 | ||
− | ||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'. |
+ | |||
|- | |- | ||
||02:52 | ||02:52 | ||
− | ||Perpendicular line and Chord 'BC' intersect at a point | + | ||Perpendicular line and Chord '''BC''' intersect at a point |
+ | |||
|- | |- | ||
||02:56 | ||02:56 | ||
− | ||Click on | + | ||Click on '''Intersect Two objects''' tool, |
|- | |- | ||
||02:58 | ||02:58 | ||
− | ||Mark the point of intersection as 'D'. | + | ||Mark the point of intersection as '''D'''. |
+ | |||
|- | |- | ||
||03:03 | ||03:03 | ||
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|- | |- | ||
||03:11 | ||03:11 | ||
− | ||Click on the points ,'B' 'D' ...'D' 'C' ... | + | ||Click on the points ,'''B''' '''D''' ...'''D''' '''C''' ... |
|- | |- | ||
||03:19 | ||03:19 | ||
− | ||Notice that distances 'BD' and 'DC' are equal. | + | ||Notice that distances '''BD''' and '''DC''' are equal. |
|- | |- | ||
||03:24 | ||03:24 | ||
− | ||It implies 'D' is midpoint of chord 'BC' | + | ||It implies '''D''' is midpoint of chord '''BC''' |
|- | |- | ||
||03:29 | ||03:29 | ||
− | ||Let's measure the angle 'CDA' | + | ||Let's measure the angle '''CDA''' |
|- | |- | ||
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|- | |- | ||
||03:35 | ||03:35 | ||
− | ||Click on the points | + | ||Click on the points '''C''','''D''', '''A''' |
|- | |- | ||
||03:42 | ||03:42 | ||
− | || angle 'CDA' is '90 degrees | + | || angle '''CDA''' is '90 degrees |
+ | |||
|- | |- | ||
||03:46 | ||03:46 | ||
− | || | + | || The Theorem is verified. |
+ | |||
|- | |- | ||
||03:50 | ||03:50 | ||
− | ||Let's Move the point 'C' and see how the distances move along with point 'C' | + | ||Let's Move the point '''C''' and see how the distances move along with point 'C' |
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|- | |- | ||
||04:05 | ||04:05 | ||
− | ||Click on | + | ||Click on '''File'''>> '''Save As''' |
|- | |- | ||
||04:08 | ||04:08 | ||
− | ||I will type the file name as | + | ||I will type the file name as '''circle-chord''' |
|- | |- | ||
||04:12 | ||04:12 | ||
− | ||circle-chord | + | ||'''circle-chord''' |
|- | |- | ||
||04:16 | ||04:16 | ||
− | || Click on Save | + | || Click on '''Save''' |
|- | |- | ||
||04:21 | ||04:21 | ||
||Let us move on to the next theorem. | ||Let us move on to the next theorem. | ||
+ | |||
|- | |- | ||
||04:28 | ||04:28 | ||
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||05:04 | ||05:04 | ||
|| and click again to get point 'B' | || and click again to get point 'B' | ||
+ | |||
|- | |- | ||
||05:10 | ||05:10 | ||
− | ||Let's draw an arc 'BC' | + | ||Let's draw an arc '''BC''' |
|- | |- | ||
||05:13 | ||05:13 | ||
− | ||Click on "'Circular Arc with Center between Two points"' | + | ||Click on "'''Circular Arc with Center between Two points"''' |
|- | |- | ||
||05:17 | ||05:17 | ||
− | ||Click on the point 'A', 'B' and 'C' on the circumference | + | ||Click on the point '''A''', '''B''' and '''C''' on the circumference |
|- | |- | ||
||05:24 | ||05:24 | ||
− | ||An Arc 'BC' is drawn | + | ||An Arc '''BC''' is drawn |
|- | |- | ||
||05:26 | ||05:26 | ||
− | ||Let's change the properties of arc 'BC' | + | ||Let's change the properties of arc '''BC''' |
|- | |- | ||
||05:30 | ||05:30 | ||
− | ||In the | + | ||In the '''Algebra View''' |
|- | |- | ||
||05:32 | ||05:32 | ||
− | ||Right click on the object 'd' | + | ||Right click on the object '''d''' |
|- | |- | ||
||05:35 | ||05:35 | ||
− | ||Select | + | ||Select '''Object Properties''' |
|- | |- | ||
||05:37 | ||05:37 | ||
− | ||Select | + | ||Select color as '''green''', click on '''Close.''' |
|- | |- | ||
||05:46 | ||05:46 | ||
− | || Click on new point tool, mark points 'D' and 'E' on the circumference of the circle. | + | || Click on '''new point tool''', mark points '''D''' and '''E''' on the circumference of the circle. |
|- | |- | ||
||05:56 | ||05:56 | ||
− | ||let's subtend two angles from arc BC to points 'D' and 'E'. | + | ||let's subtend two angles from arc BC to points '''D''' and '''E'''. |
|- | |- | ||
||06:03 | ||06:03 | ||
− | ||Click on | + | ||Click on '''Polygon''' tool, |
|- | |- | ||
||06:05 | ||06:05 | ||
− | ||click on the points 'E', 'B', 'D', 'C' and 'E' again to complete the figure. | + | ||click on the points '''E''', '''B''', '''D''', '''C''' and '''E''' again to complete the figure. |
|- | |- | ||
||06:18 | ||06:18 | ||
− | ||Let's measure the angles 'BDC' and 'BEC' | + | ||Let's measure the angles '''BDC''' and '''BEC''' |
|- | |- | ||
||06:26 | ||06:26 | ||
− | ||Click on the | + | ||Click on the '''Angle''' tool, |
|- | |- | ||
||06:28 | ||06:28 | ||
− | ||Click on points 'B', 'D', 'C' and 'B', 'E', 'C' | + | ||Click on points '''B''', '''D''', '''C''' and '''B''', '''E''', '''C''' |
|- | |- | ||
||06:40 | ||06:40 | ||
− | ||We can see that the angles 'BDC' and 'BEC' are equal. | + | ||We can see that the angles '''BDC''' and '''BEC''' are equal. |
|- | |- | ||
||06:51 | ||06:51 | ||
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|- | |- | ||
||06:55 | ||06:55 | ||
− | ||'''Angle subtended by an arc at the center, is twice the inscribed angles subtended by the same arc ''' | + | ||'''Angle subtended by an arc at the center, is twice the inscribed angles subtended by the same arc''' |
|- | |- | ||
||07:06 | ||07:06 | ||
− | ||'''Angle BAC subtended by arc BC at A is twice the inscribed angles BEC and BDC subtended by the same arc ''' | + | ||'''Angle BAC subtended by arc BC at A is twice the inscribed angles BEC and BDC subtended by the same arc''' |
|- | |- | ||
||07:22 | ||07:22 | ||
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|- | |- | ||
||07:30 | ||07:30 | ||
− | ||Click on the ' | + | ||Click on the '''Circular Sector with Center between Two Points''' tool. |
|- | |- | ||
||07:35 | ||07:35 | ||
− | ||click on the points 'A', 'B', 'C' | + | ||click on the points '''A''', '''B''', '''C''' |
|- | |- | ||
||07:45 | ||07:45 | ||
− | ||Let's change the color of sector 'ABC'. | + | ||Let's change the color of sector '''ABC'''. |
|- | |- | ||
||07:48 | ||07:48 | ||
− | ||Right click on sector 'ABC' | + | ||Right click on sector '''ABC''' |
|- | |- | ||
||07:51 | ||07:51 | ||
− | ||Select | + | ||Select '''Object Properties'''. |
|- | |- | ||
||07:54 | ||07:54 | ||
− | ||Select Color as | + | ||Select Color as '''Green'''. Click on '''Close'''. |
|- | |- | ||
||08:00 | ||08:00 | ||
− | ||Let's the measure angle 'BAC' | + | ||Let's the measure angle '''BAC''' |
|- | |- | ||
||08:04 | ||08:04 | ||
− | ||Click on the | + | ||Click on the '''Angle''' tool , Click on the points '''B''', '''A''', '''C''' |
|- | |- | ||
||08:15 | ||08:15 | ||
− | ||Angle 'BAC' is twice the angles 'BEC' and 'BDC' | + | ||Angle '''BAC''' is twice the angles '''BEC''' and '''BDC''' |
|- | |- | ||
||08:28 | ||08:28 | ||
− | ||Let's move the point 'C' | + | ||Let's move the point '''C''' |
|- | |- | ||
||08:32 | ||08:32 | ||
− | ||Notice that angle 'BAC' is always twice the angles 'BEC' and 'BDC' | + | ||Notice that angle '''BAC''' is always twice the angles '''BEC''' and '''BDC''' |
|- | |- | ||
||08:41 | ||08:41 | ||
||hence theorems are verified | ||hence theorems are verified | ||
+ | |||
|- | |- | ||
||08:45 | ||08:45 | ||
||With this we come to the end of this tutorial | ||With this we come to the end of this tutorial | ||
+ | |||
|- | |- | ||
||08:48 | ||08:48 | ||
||let's summarize | ||let's summarize | ||
+ | |||
|- | |- | ||
||08:53 | ||08:53 | ||
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||09:06 | ||09:06 | ||
||* the Central angle of a circle is twice any inscribed angle subtended by the same arc | ||* the Central angle of a circle is twice any inscribed angle subtended by the same arc | ||
+ | |||
|- | |- | ||
|| 09:15 | || 09:15 |
Revision as of 16:11, 3 September 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 | The Theorem 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 |