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

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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 ''' '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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|-
 
|-
 
||01:54
 
||01:54
−
||Select the "Circle with Center and Radius" tool from tool bar.  
+
||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  “Segment between two points” tool.  
+
||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  "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
−
||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   'C','D', 'A'  
+
||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
−
|| TheTheorem 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'
  
  
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|-
 
|-
 
||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'''
  
 
|-
 
|-
 
||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 "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'''.
  
 
|-
 
|-
 
||06:03
 
||06:03
−
||Click on "Polygon" tool,  
+
||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 "Angle" tool,   
+
||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 '"Circular Sector with Center between Two Points"' tool.
+
||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 "Object Properties".
+
||Select '''Object Properties'''.
  
 
|-
 
|-
 
||07:54
 
||07:54
−
||Select Color as “Green”. Click on "Close".
+
||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 "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 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

Contributors and Content Editors

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

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