Difference between revisions of "Geogebra/C3/Theorems-on-Chords-and-Arcs/English-timed"

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|-
 
|-
 
||00:01
 
||00:01
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||Hello,Welcome to this  tutorial on '''Theorems on Chords and Arcs in Geogebra'''
+
||Hello. Welcome to this  tutorial on '''Theorems on Chords and Arcs in Geogebra'''.
 
|-
 
|-
 
||00:08
 
||00:08
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|-
 
|-
 
||00:09
 
||00:09
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||you will be able to  verify theorems on  
+
||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, For relevant tutorials, please visit our website:  http://spoken-tutorial.org
+
||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''':  
 
      
 
      
 
|-
 
|-
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|-
 
|-
 
||00:58
 
||00:58
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||Perpendicular line  
+
||* Perpendicular line  
 
|-
 
|-
 
||01:00
 
||01:00
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|-
 
|-
 
||01:02
 
||01:02
−
||Click on  Dash home,  Media Apps.
+
||Click on  '''Dash home''',  '''Media Apps'''.
  
 
|-
 
|-
 
||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
−
||   '''Perpendicular from center of  circle to a chord bisects the chord'''
+
||"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'''
+
||Perpendicular from the center '''A''' of a circle to chord '''BC''' bisects it.
  
 
|-
 
|-
 
||01:32
 
||01:32
−
||Let's verify a theorem.
+
||Let's verify the 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'''.
  
 
|-
 
|-
 
||01:42
 
||01:42
−
||Right Click on the drawing pad  
+
||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''' on the drawing pad.
+
||Mark a point '''A''' on the drawing pad.
 
|-
 
|-
 
||02:01
 
||02:01
−
||A dialogue box   opens
+
||A dialogue box opens.
 
|-
 
|-
 
||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
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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 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  '''Perpendicular line'''  tool from tool bar
+
||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 '''Intersect Two objects'''  tool,
+
||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
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||Click on the points ,'''B''' '''D''' ...'''D''' '''C''' ...
+
||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
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||  angle '''CDA''' is '90 degrees
+
||  angle '''CDA''' is '90' degrees.
  
 
|-
 
|-
 
||03:46
 
||03:46
−
|| The Theorem is verified.
+
|| 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'.
  
 
|-
 
|-
 
||04:03
 
||04:03
−
||Let us save the file now
+
||Let us save the file now.
  
 
|-
 
|-
 
||04:05
 
||04:05
−
||Click on  '''File'''>> '''Save As'''
+
||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.'''    
+
||"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'''   
+
||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'sOpen a new Geogebra window,
+
||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 circle
+
||Let's draw a circle.
  
 
|-
 
|-
 
||04:57
 
||04:57
−
||Click on '''the Circle with Center through Point''' tool from toolbar
+
||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 "'''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 points '''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 '''Algebra View'''  
+
||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  '''Object Properties'''
+
||Select  '''Object Properties'''.
  
 
|-
 
|-
 
||05:37
 
||05:37
−
||Select color as '''green''',  click on '''Close.'''
+
||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'''.
  
 
|-
 
|-
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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'''    
+
||"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
−
||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'''
+
||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'''.
  
 
|-
 
|-
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|-
 
|-
 
||08:00
 
||08:00
−
||Let's the measure angle '''BAC'''
+
||Let's measure the angle '''BAC'''.
  
 
|-
 
|-
 
||08:04  
 
||08:04  
−
||Click on  the '''Angle''' tool , Click on the points '''B''', '''A''', '''C'''
+
||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 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
+
||Let's summarize.
  
 
|-
 
|-
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|-
 
|-
 
||08:57
 
||08:57
−
||*  Perpendicular   from center to a  chord bisects it  
+
||*  Perpendicular from center to a  chord bisects it  
  
 
|-
 
|-
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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
−
|| As an assignment  I would like you to verify  
+
|| As an assignment, I would like you to verify  
  
 
|-
 
|-
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|-
 
|-
 
||09:25
 
||09:25
−
||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  output should look like this
+
||Assignment  output should look like this.
 
|-
 
|-
 
||09:48
 
||09:48
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|-
 
|-
 
||09:51
 
||09:51
−
||It summarises the Spoken Tutorial project  
+
||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 Mission is available at this link
+
||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.

Revision as of 08:18, 24 February 2015

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 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 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'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.
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 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.

Contributors and Content Editors

Madhurig, PoojaMoolya, Pratik kamble, Sandhya.np14, Sneha

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