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

||Hello,Welcome to this  tutorial on '''Theorems on Chords and Arcs in Geogebra'''

||At the end of this  tutorial,  

||00:10

||you will be able to  verify theorems on

||00:19

||We assume that you have the basic working knowledge of Geogebra.   

||If not,For relevant tutorials, please visit our website http://spoken-tutorial.org

||To record this tutorial I am using   

||00:33

||Ubuntu Linux OS Version  11.10  Geogebra Version 3.2.47.0  

|00:43

||We will use the following Geogebra tools   

||* Circle with Center and Radius  

||00:50

||* Circular Sector with Center between Two Points

||* Circular Arc with Center between Two points

||* Midpoint  and

*Perpendicular line  

||Click on  Dash home  Media Apps.

||01:07

||Under Type Choose Education and  GeoGebra.

||Let's state a  theorem

|| 01:18

||   '''Perpendicular from center of  circle to a chord bisects the chord'''

||'''Perpendicular from center A   of a circle to chord BC bisects it'''

||Let's verify a theorem.

||For this tutorial I will use 'Grid layout' instead of Axes

||Right Click on the drawing pad  

||In the 'Graphic view'  

 

||uncheck 'Axes' and

||Select 'Grid'

||01:52

||Select the "Circle with Center and Radius" tool from tool bar.  

||Mark a point 'A' on the drawing pad.

||A dialogue box   open

||Let's type value '3' for radius  

||Click OK.

||A Circle with center 'A' and radius '3cm' is drawn

||02:14

||Let's Move the  point 'A' and  see the movement of the circle.

||Select  “Segment between two points” tool.  

||Mark points 'B'  and 'C'  on the circumference of the circle  

||A chord 'BC' is drawn.

||Let's draw a  perpendicular line to Chord 'BC' which passes through point 'A'.

||02:36

||Click on  "Perpendicular line" tool from tool bar

||Click on  the chord  'BC', and point 'A'.

||02:45

||Let's Move the  point 'B', and see how the perpendicular line moves along with point 'B'.

||Perpendicular line and Chord 'BC' intersect at a point  

||02:59

||Mark the point of intersection as 'D'.

||03:04

||Let's verify whether D is the mid point of chord BC

||03:09

||Click on the "Distance"  tool...

||03:12

||Click on the points ,'B' 'D' ...'D' 'C' ...

||Notice that distances 'BD' and 'DC' are equal.

||It implies 'D' is midpoint of  chord 'BC'

||Let's measure the angle 'CDA'  

||Click on Angle tool ...

||03:36

||Click on the points   'C','D', 'A'  

|| angle 'CDA' is '90^0'.

|| TheTheorem is verified.

||Let's Move the point  'C'  

||03:52

||and see how the distances move along with point 'C'

||Click on  “File”>> "Save As"

||I will type the file name as "circle-chord" click on “Save”

||'''Inscribed angles subtended by the same arc are equal.'''    

||'''Inscribed angles BDC and BEC subtended by the same arc BC are equal'''   

||04:54

||Let'sOpen a new Geogebra window,

||Click on “File” >> "New"

||Let's draw a ''circle''

||Click on " the Circle with Center through point tool from toolbar"

||Mark a point A' as centre  

|| and click again to get point 'B' and 'C' on the circumference

||05:09

||Let's draw an arc 'BC'

||Click on "Circular Arc with Center between Two points"

||05:18

||Click on the point 'A'B' and 'C' on the circumference  

 

 

||An Arc 'BC' is drawn  

||05:27

||Let's change the  properties of arc 'BC'

||In the "Algebra View"

||Right click on the object 'd'

||Select  "Object Properties"

||05:38

||Select '' color'' as ''green'' click on close.

|| Click on new point tool, mark points  'D' and 'E' on the circumference of the circle.

||let's subtend two angles from arc BC to points  'D' And 'E'.

||06:04

||Click on "Polygon" tool,  

||click on the  points  'E', 'B', 'D', 'C' and 'E'  again to complete the figure.

||Let's measure the angles  'BDC'  and 'BEC'  

||06:27

||Click on the "Angle" tool,   

||06:29

||Click  on points  'B', 'D', 'C' and    'B', 'E', 'C'

||We can see that the angles  'BDC'  and  'BEC' are equal.

||06:52

||Let's state a next theorem

||'''Angle subtended by an arc at the center, is twice the inscribed angles 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 '''

||Let's verify the theorem

||Let's draw a sector 'ABC'

||Click on the "Circular Sector with Center between Two Points" tool.

||click on the  points 'A', 'B', 'C'

||Let's change the color of   sector 'ABC'.

||Right click on sector 'ABC'

||Select "Object Properties".

||Select Color as “Green”. Click on "Close".

||Let's the measure angle 'BAC'

||Click on  the "Angle" tool , Click on the points 'B', 'A', 'C'

||Angle  'BAC' is twice the angles  'BEC' and 'BDC'

||Let's move the point 'C'

||Notice that  angle  'BAC' is always twice the angles  'BEC' and 'BDC'

||hence theorems  are verified

||With this we come to the end of the tutorial  

||let's summarize

||*  Perpendicular   from center to a  chord bisects it  

||*  Inscribed angles subtended by the same  arc  are equal  

||* the Central angle of a circle is twice any inscribed angle subtended by the same arc

|| As an assignment  I would like you to verify  

||Draw a circle.  

 

||Select Segment with Given length from point tool  

||Assignment  out put should look like this

||Watch the video available at this url  http://spoken-tutorial.org/What is a Spoken Tutorial  

||It summarises the Spoken Tutorial project  

||If you do not have good bandwidth, you can download and watch it  

||Conducts workshops using spoken tutorials  

||Gives certificates to those who pass an online test  

||10:07

||For more details, please write to contact@spoken-tutorial.org

||Spoken Tutorial Project is a part  of the Talk to a Teacher project  

||It is supported by the National Mission on Education through ICT, MHRD, Government of India  

||More information on this Mission is available at http://spoken-tutorial.org/NMEICT-Intro ]

||This is Madhuri Ganapathi from IIT Bombay signing off .Thank you  for joining