Difference between revisions of "Geogebra/C3/Theorems-on-Chords-and-Arcs/English-timed"
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||00:01 | ||00:01 | ||
− | ||Hello | + | ||Hello. Welcome to this tutorial on '''Theorems on Chords and Arcs in Geogebra'''. |
|- | |- | ||
||00:08 | ||00:08 | ||
− | ||At the end of this tutorial, | + | ||At the end of this tutorial, you will be able to verify theorems on: |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
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||00:18 | ||00:18 | ||
− | ||We assume that you have the basic working knowledge of Geogebra. | + | ||We assume that you have the basic working knowledge of '''Geogebra'''. |
|- | |- | ||
||00:23 | ||00:23 | ||
− | ||If not, | + | ||If not, for relevant tutorials, please visit our website: http://spoken-tutorial.org |
|- | |- | ||
|| 00:30 | || 00:30 | ||
− | ||To record this tutorial I am using | + | ||To record this tutorial I am using: |
|- | |- | ||
||00:32 | ||00:32 | ||
− | ||Ubuntu Linux OS Version 11.10 | + | ||'''Ubuntu Linux OS''' Version 11.10 |
|- | |- | ||
||00:36 | ||00:36 | ||
− | ||Geogebra Version 3.2.47.0 | + | ||'''Geogebra''' Version 3.2.47.0 |
|- | |- | ||
|00:42 | |00:42 | ||
− | ||We will use the following Geogebra tools | + | ||We will use the following '''Geogebra tools''': |
|- | |- | ||
||00:47 | ||00:47 | ||
− | || | + | ||Circle with Center and Radius |
|- | |- | ||
||00:49 | ||00:49 | ||
− | || | + | ||Circular Sector with Center between Two Points |
|- | |- | ||
||00:53 | ||00:53 | ||
− | || | + | ||Circular Arc with Center between Two points |
|- | |- | ||
||00:56 | ||00:56 | ||
− | || | + | ||Midpoint and |
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||01:02 | ||01:02 | ||
− | ||Click on Dash | + | ||Click on '''Dash home''', '''Media Apps'''. |
|- | |- | ||
||01:06 | ||01:06 | ||
− | ||Under Type | + | ||Under '''Type''', choose '''Education''' and '''GeoGebra'''. |
|- | |- | ||
||01:15 | ||01:15 | ||
− | ||Let's state a theorem | + | ||Let's state a theorem: |
|- | |- | ||
|| 01:17 | || 01:17 | ||
− | || | + | ||"Perpendicular from center of circle to a chord bisects the chord". |
|- | |- | ||
||01:23 | ||01:23 | ||
− | || | + | ||Perpendicular from the center '''A''' of a circle to chord '''BC''' bisects it. |
|- | |- | ||
||01:32 | ||01:32 | ||
− | ||Let's verify | + | ||Let's verify the theorem. |
|- | |- | ||
||01:37 | ||01:37 | ||
− | ||For this tutorial | + | ||For this tutorial, I will use '''Grid''' layout instead of '''Axes'''. |
|- | |- | ||
||01:42 | ||01:42 | ||
− | ||Right | + | ||Right click on the drawing pad. |
|- | |- | ||
||01:44 | ||01:44 | ||
− | ||In the '''Graphic view''' uncheck '''Axes''' | + | ||In the '''Graphic view''', uncheck '''Axes'''. |
|- | |- | ||
||01:47 | ||01:47 | ||
− | ||Select '''Grid''' | + | ||Select '''Grid'''. |
+ | |||
|- | |- | ||
||01:51 | ||01:51 | ||
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|- | |- | ||
||01:58 | ||01:58 | ||
− | ||Mark a point '''A''' | + | ||Mark a point '''A''' on the drawing pad. |
|- | |- | ||
||02:01 | ||02:01 | ||
− | ||A | + | ||A dialog box opens. |
|- | |- | ||
||02:03 | ||02:03 | ||
− | ||Let's type value '''3''' for radius | + | ||Let's type value '''3''' for radius. |
|- | |- | ||
||02:06 | ||02:06 | ||
− | ||Click OK. | + | ||Click '''OK'''. A circle with center '''A''' and radius '''3cm''' is drawn. |
− | + | ||
− | + | ||
− | + | ||
|- | |- | ||
||02:13 | ||02:13 | ||
− | ||Let's | + | ||Let's move the point '''A''' and see the movement of the circle. |
|- | |- | ||
||02:19 | ||02:19 | ||
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||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. |
|- | |- | ||
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||02:30 | ||02:30 | ||
− | ||Let's draw a perpendicular line to | + | ||Let's draw a perpendicular line to chord '''BC''' which passes through point '''A'''. |
|- | |- | ||
||02:35 | ||02:35 | ||
− | ||Click on '''Perpendicular | + | ||Click on '''Perpendicular Line''' tool from tool bar. |
|- | |- | ||
||02:39 | ||02:39 | ||
− | ||Click on the chord '''BC''' | + | ||Click on the chord '''BC''' and point '''A'''. |
|- | |- | ||
||02:44 | ||02:44 | ||
− | ||Let's | + | ||Let's move the point '''B''' and see how the perpendicular line moves along with point 'B'. |
|- | |- | ||
||02:52 | ||02:52 | ||
− | ||Perpendicular line and | + | ||Perpendicular line and chord '''BC''' intersect at a point. |
|- | |- | ||
||02:56 | ||02:56 | ||
− | ||Click on '''Intersect Two | + | ||Click on '''Intersect Two Objects''' tool. |
− | + | ||
|- | |- | ||
||02:58 | ||02:58 | ||
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||03:03 | ||03:03 | ||
− | ||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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||03:11 | ||03:11 | ||
− | ||Click on the points | + | ||Click on the points '''B''', '''D''' ...'''D''', '''C''' . |
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||03:29 | ||03:29 | ||
− | ||Let's measure the angle '''CDA''' | + | ||Let's measure the angle '''CDA'''. |
|- | |- | ||
||03:33 | ||03:33 | ||
− | ||Click on Angle tool | + | ||Click on '''Angle''' tool. |
|- | |- | ||
||03:35 | ||03:35 | ||
− | ||Click on the points '''C''','''D''', '''A''' | + | ||Click on the points '''C''', '''D''', '''A''', |
|- | |- | ||
||03:42 | ||03:42 | ||
− | || | + | ||angle '''CDA''' is '90' degrees. |
|- | |- | ||
||03:46 | ||03:46 | ||
− | || The | + | || The theorem is verified. |
|- | |- | ||
||03:50 | ||03:50 | ||
− | ||Let's | + | ||Let's move the point '''C''' and see how the distances move along with point 'C'. |
|- | |- | ||
||04:03 | ||04:03 | ||
− | ||Let us save the file now | + | ||Let us save the file now. |
|- | |- | ||
||04:05 | ||04:05 | ||
− | ||Click on '''File'''>> | + | ||Click on '''File''' >> '''Save As'''. |
|- | |- | ||
||04:08 | ||04:08 | ||
− | ||I will type the file name as '''circle-chord''' | + | ||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'''. |
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||04:28 | ||04:28 | ||
− | || | + | ||"Inscribed angles subtended by the same arc are equal". |
|- | |- | ||
||04:34 | ||04:34 | ||
− | ||''' | + | ||Inscribed angles '''BDC''' and '''BEC''' subtended by the same arc '''BC''' are equal. |
|- | |- | ||
||04:44 | ||04:44 | ||
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||04:48 | ||04:48 | ||
− | ||Let' | + | ||Let's open a new Geogebra window. |
|- | |- | ||
||04:51 | ||04:51 | ||
− | ||Click on '''File''' >> '''New''' | + | ||Click on '''File''' >> '''New'''. |
|- | |- | ||
||04:55 | ||04:55 | ||
− | ||Let's draw a | + | ||Let's draw a circle. |
|- | |- | ||
||04:57 | ||04:57 | ||
− | ||Click on ''' | + | ||Click on '''Circle with Center through Point''' tool, from toolbar. |
|- | |- | ||
||05:01 | ||05:01 | ||
− | ||Mark a point A' as centre | + | ||Mark a point '''A''' as centre, |
|- | |- | ||
||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 | + | ||Click on '''Circular Arc with Center between Two Points'''. |
|- | |- | ||
||05:17 | ||05:17 | ||
− | ||Click on the | + | ||Click on the points '''A''', '''B''' and '''C''' on the circumference. |
|- | |- | ||
||05:24 | ||05:24 | ||
− | ||An | + | ||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 '''Algebra View''' | + | ||In the '''Algebra View''', |
|- | |- | ||
||05:32 | ||05:32 | ||
− | || | + | ||right click on the object '''d'''. |
|- | |- | ||
||05:35 | ||05:35 | ||
− | ||Select '''Object Properties''' | + | ||Select '''Object Properties'''. |
|- | |- | ||
||05:37 | ||05:37 | ||
− | ||Select | + | ||Select Color as '''green''', click on '''Close.''' |
|- | |- | ||
||05:46 | ||05:46 | ||
− | || Click on ''' | + | || 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'''. |
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||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'''. |
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||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 | ||
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||06:51 | ||06:51 | ||
− | ||Let's state a next theorem | + | ||Let's state a next theorem. |
|- | |- | ||
||06:55 | ||06:55 | ||
− | || | + | ||"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. |
|- | |- | ||
||07:22 | ||07:22 | ||
− | ||Let's verify the theorem | + | ||Let's verify the theorem. |
|- | |- | ||
||07:26 | ||07:26 | ||
− | ||Let's draw a sector '''ABC''' | + | ||Let's draw a sector '''ABC'''. |
|- | |- | ||
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||07:35 | ||07:35 | ||
− | || | + | ||Click on the points '''A''', '''B''', '''C'''. |
|- | |- | ||
||07:45 | ||07:45 | ||
− | ||Let's change the color of | + | ||Let's change the color of sector '''ABC'''. |
|- | |- | ||
||07:48 | ||07:48 | ||
− | ||Right click on sector '''ABC''' | + | ||Right click on sector '''ABC'''. |
|- | |- | ||
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||08:00 | ||08:00 | ||
− | ||Let's | + | ||Let's measure the angle '''BAC'''. |
|- | |- | ||
||08:04 | ||08:04 | ||
− | ||Click on the '''Angle''' tool , | + | ||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 the 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. |
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||08:57 | ||08:57 | ||
− | || | + | ||Perpendicular from center to a chord bisects it |
|- | |- | ||
||09:00 | ||09:00 | ||
− | || | + | ||Inscribed angles subtended by the same arc are equal |
|- | |- | ||
||09:06 | ||09:06 | ||
− | || | + | ||the Central angle of a circle is twice any inscribed angle subtended by the same arc. |
|- | |- | ||
|| 09:15 | || 09:15 | ||
− | || As an assignment I would like you to verify | + | || As an assignment, I would like you to verify |
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||09:24 | ||09:24 | ||
− | ||Draw a circle. | + | ||Draw a circle. Select Segment with given length from point tool. |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
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||09:44 | ||09:44 | ||
− | ||Assignment output should look like this | + | ||Assignment output should look like this. |
|- | |- | ||
||09:48 | ||09:48 | ||
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||09:51 | ||09:51 | ||
− | ||It | + | ||It summarizes the Spoken Tutorial project. |
|- | |- | ||
||09:53 | ||09:53 | ||
− | ||If you do not have good bandwidth, you can download and watch it | + | ||If you do not have good bandwidth, you can download and watch it. |
|- | |- | ||
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||10:00 | ||10:00 | ||
− | ||Conducts workshops using spoken tutorials | + | ||Conducts workshops using spoken tutorials. |
|- | |- | ||
||10:03 | ||10:03 | ||
− | ||Gives certificates to those who pass an online test | + | ||Gives certificates to those who pass an online test. |
|- | |- | ||
||10:06 | ||10:06 | ||
− | ||For more details, please write to contact@spoken-tutorial.org | + | ||For more details, please write to contact@spoken-tutorial.org. |
|- | |- | ||
||10:14 | ||10:14 | ||
− | ||Spoken Tutorial Project is a part of the Talk to a Teacher project | + | ||Spoken Tutorial Project is a part of the Talk to a Teacher project. |
|- | |- | ||
||10:18 | ||10:18 | ||
− | ||It is supported by the National Mission on Education through ICT, MHRD, Government of India | + | ||It is supported by the National Mission on Education through ICT, MHRD, Government of India. |
|- | |- | ||
||10:25 | ||10:25 | ||
− | ||More information on this | + | ||More information on this mission is available at this link. |
|- | |- | ||
||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. |
Latest revision as of 14:48, 28 October 2020
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, 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 the 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 dialog box opens. |
02:03 | Let's type value 3 for radius. |
02:06 | Click OK. 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's open a new Geogebra window. |
04:51 | Click on File >> New. |
04:55 | Let's draw a circle. |
04:57 | Click on 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 points 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 measure the 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 the 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. 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 summarizes 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. |