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

From Script | Spoken-Tutorial
Jump to: navigation, search
Line 10: Line 10:
  
 
|-
 
|-
−
||00:10
+
||00:09
 
||you will be able to  verify theorems on  
 
||you will be able to  verify theorems on  
  
−
*Chords of circle.
+
|-
 +
||00:14
 +
||Chords of circle.
  
−
* Arcs of circle.
 
 
|-
 
|-
−
||00:19
+
||00:16
 +
|| Arcs of circle.
 +
|-
 +
||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
Line 28: Line 32:
  
 
|-
 
|-
−
||00:33
+
||00:32
−
||Ubuntu Linux OS Version  11.10  Geogebra Version 3.2.47.0  
+
||Ubuntu Linux OS Version  11.10   
 +
 
 +
|-
 +
||00:36
 +
||Geogebra Version 3.2.47.0  
 +
 
 
|-
 
|-
−
|00:43
+
|00:42
 
||We will use the following Geogebra tools   
 
||We will use the following Geogebra tools   
 
      
 
      
Line 39: Line 48:
  
 
|-
 
|-
−
||00:50
+
||00:49
 
||* Circular Sector with Center between Two Points
 
||* Circular Sector with Center between Two Points
  
Line 50: Line 59:
 
||* Midpoint  and
 
||* Midpoint  and
  
−
*Perpendicular line  
+
|-
 +
||00:58
 +
||Perpendicular line  
 
|-
 
|-
 
||01:00
 
||01:00
Line 57: Line 68:
 
|-
 
|-
 
||01:02
 
||01:02
−
||Click on  Dash  home  Media Apps.
+
||Click on  Dash  home, Media Apps.
  
 
|-
 
|-
−
||01:07
+
||01:06
 
||Under Type Choose Education and  GeoGebra.
 
||Under Type Choose Education and  GeoGebra.
 
|-
 
|-
Line 66: Line 77:
 
||Let's state a  theorem
 
||Let's state a  theorem
 
|-
 
|-
−
|| 01:18
+
|| 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 center A  of a circle to chord BC bisects it'''
+
||'''Perpendicular from the center A  of a circle to chord BC bisects it'''
  
 
|-
 
|-
Line 86: Line 97:
 
|-
 
|-
 
||01:44
 
||01:44
−
||In the 'Graphic view'  
+
||In the ''' 'Graphic view' ''' uncheck  ''' 'Axes' '''
−
 
+
−
|-
+
−
||01:45
+
−
||uncheck  'Axes' and
+
  
 
|-
 
|-
Line 96: Line 103:
 
||Select 'Grid'
 
||Select 'Grid'
 
|-
 
|-
−
||01:52
+
||01:51
 
||Let's draw a circle.
 
||Let's draw a circle.
  
Line 108: Line 115:
 
|-
 
|-
 
||02:01
 
||02:01
−
||A dialogue box  open
+
||A dialogue box  opens
 
|-
 
|-
 
||02:03
 
||02:03
Line 121: Line 128:
  
 
|-
 
|-
−
||02:14
+
||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.
 
|-
 
|-
Line 139: Line 146:
  
 
|-
 
|-
−
||02:36
+
||02:35
 
||Click on  "Perpendicular line"  tool from tool bar
 
||Click on  "Perpendicular line"  tool from tool bar
  
Line 146: Line 153:
 
||Click on  the chord  'BC', and point 'A'.
 
||Click on  the chord  'BC', and point 'A'.
 
|-
 
|-
−
||02:45
+
||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'.
 
|-
 
|-
Line 152: Line 159:
 
||Perpendicular line and Chord 'BC' intersect at a point  
 
||Perpendicular line and Chord 'BC' intersect at a point  
 
|-
 
|-
−
||02:57
+
||02:56
 
||Click on “Intersect Two objects”  tool,
 
||Click on “Intersect Two objects”  tool,
  
 
|-
 
|-
−
||02:59
+
||02:58
 
||Mark the point of intersection as 'D'.
 
||Mark the point of intersection as 'D'.
 
|-
 
|-
−
||03:04
+
||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
 +
 
|-
 
|-
−
||03:09
+
||03:08
−
||Click on the "Distance"  tool...
+
||Click on the "Distance"  tool.
  
 
|-
 
|-
−
||03:12
+
||03:11
 
||Click on the points ,'B'  'D' ...'D'  'C' ...
 
||Click on the points ,'B'  'D' ...'D'  'C' ...
  
Line 185: Line 193:
  
 
|-
 
|-
−
||03:36
+
||03:35
 
||Click on the points    'C','D', 'A'  
 
||Click on the points    'C','D', 'A'  
  
 
|-
 
|-
 
||03:42
 
||03:42
−
||  angle 'CDA' is '90^0'.
+
||  angle 'CDA' is '90 degrees
 
|-
 
|-
 
||03:46
 
||03:46
Line 196: Line 204:
 
|-
 
|-
 
||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'
  
−
|-
 
−
||03:52
 
−
||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
Line 211: Line 217:
 
|-
 
|-
 
||04:08
 
||04:08
−
||I will type the file name as "circle-chord" click on “Save”
+
||I will type the file name as "circle-chord"  
 +
 
 +
|-
 +
||04:12
 +
||circle-chord
 +
 
 +
|-
 +
||04:16
 +
|| Click on Save
 +
 
 
|-
 
|-
 
||04:21
 
||04:21
Line 226: Line 241:
 
||Let's verify the theorem.
 
||Let's verify the theorem.
 
|-
 
|-
−
||04:54
+
||04:48
 
||Let'sOpen a new Geogebra window,
 
||Let'sOpen a new Geogebra window,
  
Line 238: Line 253:
 
|-
 
|-
 
||04:57
 
||04:57
−
||Click on " the Circle with Center through point tool from toolbar"
+
||Click on "' the Circle with Center through Point''' tool from toolbar
  
 
|-
 
|-
Line 246: Line 261:
 
|-
 
|-
 
||05:04
 
||05:04
−
|| and click again to get point 'B' and 'C'  on the circumference
+
|| and click again to get point 'B'  
 
|-
 
|-
−
||05:09
+
||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"'
  
 
|-
 
|-
−
||05:18
+
||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  
 +
 
|-
 
|-
−
||05:27
+
||05:26
 
||Let's change the  properties of arc 'BC'
 
||Let's change the  properties of arc 'BC'
 
|-
 
|-
Line 280: Line 294:
  
 
|-
 
|-
−
||05:38
+
||05:37
−
||Select '' color'' as ''green'' click on close.
+
||Select '' color'' as ''green'',  click on '''Close.'''
 
|-
 
|-
 
||05:46
 
||05:46
Line 288: Line 302:
 
|-
 
|-
 
||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'.
  
 
|-
 
|-
−
||06:04
+
||06:03
 
||Click on "Polygon" tool,  
 
||Click on "Polygon" tool,  
 
|-
 
|-
Line 301: Line 315:
  
 
|-
 
|-
−
||06:27
+
||06:26
 
||Click on the "Angle" tool,   
 
||Click on the "Angle" tool,   
  
 
|-
 
|-
−
||06:29
+
||06:28
 
||Click  on points  'B', 'D', 'C' and    'B', 'E', 'C'
 
||Click  on points  'B', 'D', 'C' and    'B', 'E', 'C'
 
|-
 
|-
Line 311: Line 325:
 
||We can see that the angles  'BDC'  and  'BEC' are equal.
 
||We can see that the angles  'BDC'  and  'BEC' are equal.
 
|-
 
|-
−
||06:52
+
||06:51
 
||Let's state a next theorem
 
||Let's state a next theorem
 
|-
 
|-
Line 328: Line 342:
 
|-
 
|-
 
||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.
  
 
|-
 
|-
Line 372: Line 386:
 
|-
 
|-
 
||08:45
 
||08:45
−
||With this we come to the end of the tutorial  
+
||With this we come to the end of this tutorial  
 
|-
 
|-
 
||08:48
 
||08:48
Line 404: Line 418:
  
 
|-
 
|-
−
||09:26
+
||09:25
 
||Select Segment with Given length from point tool  
 
||Select Segment with Given length from point tool  
  
Line 424: Line 438:
 
|-
 
|-
 
||09:44
 
||09:44
−
||Assignment  out put should look like this
+
||Assignment  output should look like this
 
|-
 
|-
 
||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  
  
 
|-
 
|-
Line 450: Line 464:
  
 
|-
 
|-
−
||10:07
+
||10:06
 
||For more details, please write to contact@spoken-tutorial.org
 
||For more details, please write to contact@spoken-tutorial.org
 
|-
 
|-
Line 462: Line 476:
 
|-
 
|-
 
||10:25
 
||10:25
−
||More information on this Mission is available at http://spoken-tutorial.org/NMEICT-Intro ]
+
||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 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

Contributors and Content Editors

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

Retrieved from "https://script.spoken-tutorial.org/index.php?title=Geogebra/C3/Theorems-on-Chords-and-Arcs/English-timed&oldid=15545"