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

|'''Narration'''   

|'''Narration'''   

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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'''

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||At the end of this  tutorial,  

||At the end of this  tutorial,  

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||you will be able to  verify theorems on  

||you will be able to  verify theorems on  

* Arcs of circle.

* Arcs of circle.

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

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

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||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

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||To record this tutorial I am using   

||To record this tutorial I am using   

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||Ubuntu Linux OS Version  11.10  Geogebra Version 3.2.47.0  

||Ubuntu Linux OS Version  11.10  Geogebra Version 3.2.47.0  

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||We will use the following Geogebra tools   

||We will use the following Geogebra tools   

      

      

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||* Circle with Center and Radius  

||* Circle with Center and Radius  

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||* Circular Sector with Center between Two Points

||* Circular Sector with Center between Two Points

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||* Circular Arc with Center between Two points

||* Circular Arc with Center between Two points

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||* Midpoint  and

||* Midpoint  and

*Perpendicular line  

*Perpendicular line  

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||Let's open a new  GeoGebra window.

||Let's open a new  GeoGebra window.

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||Click on  Dash  home  Media Apps.

||Click on  Dash  home  Media Apps.

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||Under Type Choose Education and  GeoGebra.

||Under Type Choose Education and  GeoGebra.

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||Let's state a  theorem

||Let's state a  theorem

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

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

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

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

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||Let's verify a theorem.

||Let's verify a theorem.

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||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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||Right Click on the drawing pad  

||Right Click on the drawing pad  

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||In the 'Graphic view'  

||In the 'Graphic view'  

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||uncheck  'Axes' and

||uncheck  'Axes' and

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||Select 'Grid'

||Select 'Grid'

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||Let's draw a circle.

||Let's draw a circle.

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

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

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

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

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||A dialogue box  open

||A dialogue box  open

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||Let's type value '3' for radius  

||Let's type value '3' for radius  

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||Click OK.

||Click OK.

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

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

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||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.

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||Select  “Segment between two points” tool.  

||Select  “Segment between two points” tool.  

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||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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||A chord 'BC' is drawn.

||A chord 'BC' is drawn.

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||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'.

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

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

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

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

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||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'.

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

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

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||Click on “Intersect Two objects”  tool,

||Click on “Intersect Two objects”  tool,

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

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

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||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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||Click on the "Distance"  tool...

||Click on the "Distance"  tool...

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

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

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

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

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

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

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||Let's measure the angle 'CDA'  

||Let's measure the angle 'CDA'  

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||Click on Angle tool  ...

||Click on Angle tool  ...

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

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

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||  angle 'CDA' is '90^0'.

||  angle 'CDA' is '90^0'.

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|| TheTheorem is verified.

|| TheTheorem is verified.

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||Let's Move the point  'C'  

||Let's Move the point  'C'  

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

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

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||Let us save the file now

||Let us save the file now

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||Click on  “File”>>  "Save As"

||Click on  “File”>>  "Save As"

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

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

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||Let us move on to the next theorem.

||Let us move on to the next theorem.

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

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

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||'''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'''   

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||Let's verify the theorem.

||Let's verify the theorem.

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||Let'sOpen a new Geogebra window,

||Let'sOpen a new Geogebra window,

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||Click on “File” >> "New"

||Click on “File” >> "New"

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||Let's draw a  ''circle''

||Let's draw a  ''circle''

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

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

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||Mark a point A' as centre  

||Mark a point A' as centre  

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

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

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||Let's draw an arc 'BC'

||Let's draw an arc 'BC'

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

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

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

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

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||An Arc 'BC' is drawn  

||An Arc 'BC' is drawn  

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

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

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||In the "Algebra View"  

||In the "Algebra View"  

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||Right click on the object 'd'

||Right click on the object 'd'

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||Select  "Object Properties"

||Select  "Object Properties"

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

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

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|| 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.

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||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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||Click on "Polygon" tool,  

||Click on "Polygon" tool,  

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||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.

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

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

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||Click on the "Angle" tool,   

||Click on the "Angle" tool,   

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

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

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

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

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||Let's state a next theorem

||Let's state a next theorem

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||'''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 '''   

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||'''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 '''

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||Let's verify the theorem

||Let's verify the theorem

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||Let's draw a sector 'ABC'

||Let's draw a sector 'ABC'

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

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

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||click on the  points 'A',  'B', 'C'

||click on the  points 'A',  'B', 'C'

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

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

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||Right click on sector 'ABC'

||Right click on sector 'ABC'

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||Select "Object Properties".

||Select "Object Properties".

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

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

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||Let's the measure angle 'BAC'

||Let's the measure angle 'BAC'

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

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

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

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

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||Let's move the point 'C'

||Let's move the point 'C'

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

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

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||hence theorems  are verified

||hence theorems  are verified

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

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

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||let's summarize

||let's summarize

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||In this tutorial, we have learnt to verify that:

||In this tutorial, we have learnt to verify that:

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||*  Perpendicular  from center to a  chord bisects it  

||*  Perpendicular  from center to a  chord bisects it  

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

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

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||* 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

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|| As an assignment  I would like you to verify  

|| As an assignment  I would like you to verify  

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||Equal chords of a circle are equidistant from center.

||Equal chords of a circle are equidistant from center.

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||Draw a circle.  

||Draw a circle.  

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||Select Segment with Given length from point tool  

||Select Segment with Given length from point tool  

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||Use it to draw two chords of equal size.  

||Use it to draw two chords of equal size.  

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||Draw perpendicular lines from center  to chords.

||Draw perpendicular lines from center  to chords.

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||Mark points of intersection.  

||Mark points of intersection.  

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||Measure  perpendicular distances.  

||Measure  perpendicular distances.  

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||Assignment  out put should look like this

||Assignment  out put should look like this

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||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  

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||It summarises the Spoken Tutorial project  

||It summarises the Spoken Tutorial project  

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||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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||The Spoken Tutorial Project Team :

||The Spoken Tutorial Project Team :

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||Conducts workshops using spoken tutorials  

||Conducts workshops using spoken tutorials  

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||Gives certificates to those who pass an online test  

||Gives certificates to those who pass an online test  

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

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

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||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  

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||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  

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

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

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||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