Difference between revisions of "Geogebra/C3/Theorems-on-Chords-and-Arcs/English-timed"
From Script | Spoken-Tutorial
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|'''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 | ||
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* 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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− | ||01 | + | ||01:32 |
||Let's verify a theorem. | ||Let's verify a theorem. | ||
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− | ||01 | + | ||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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||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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− | ||01 | + | ||01:52 |
||Let's draw a circle. | ||Let's draw a circle. | ||
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− | ||01 | + | ||01:54 |
||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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− | ||02 | + | ||02:19 |
||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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− | ||03 | + | ||03:33 |
||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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− | ||03 | + | ||03:52 |
||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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− | ||04 | + | ||04:21 |
||Let us move on to the next theorem. | ||Let us move on to the next theorem. | ||
|- | |- | ||
− | ||04 | + | ||04:28 |
||'''Inscribed angles subtended by the same arc are equal.''' | ||'''Inscribed angles subtended by the same arc are equal.''' | ||
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− | ||04 | + | ||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''' | ||
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− | ||04 | + | ||04:44 |
||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" | ||
|- | |- | ||
− | ||04 | + | ||04:55 |
||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 | ||
Line 262: | Line 262: | ||
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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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− | ||07 | + | ||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 ''' | ||
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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 | ||
|- | |- | ||
− | ||09 | + | ||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 | ||
|- | |- | ||
− | ||09 | + | ||09:51 |
||It summarises the Spoken Tutorial project | ||It summarises the Spoken Tutorial project | ||
|- | |- | ||
− | ||09 | + | ||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 | ||
|- | |- | ||
− | ||09 | + | ||09:58 |
||The Spoken Tutorial Project Team : | ||The Spoken Tutorial Project Team : | ||
|- | |- | ||
− | ||10 | + | ||10:00 |
||Conducts workshops using spoken tutorials | ||Conducts workshops using spoken tutorials | ||
|- | |- | ||
− | ||10 | + | ||10:03 |
||Gives certificates to those who pass an online test | ||Gives certificates to those who pass an online test | ||
|- | |- | ||
− | ||10 | + | ||10:07 |
||For more details, please write to contact@spoken-tutorial.org | ||For more details, please write to contact@spoken-tutorial.org | ||
|- | |- | ||
− | ||10 | + | ||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 | + | ||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 | + | ||10:25 |
||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 ] | ||
|- | |- | ||
− | ||10 | + | ||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 12:24, 9 July 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, |
00:10 | you will be able to verify theorems on
*Chords of circle.
|
00:19 | 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 |
00:33 | Ubuntu Linux OS Version 11.10 Geogebra Version 3.2.47.0 |
00:43 | We will use the following Geogebra tools |
00:47 | * Circle with Center and Radius |
00:50 | * Circular Sector with Center between Two Points |
00:53 | * Circular Arc with Center between Two points |
00:56 | * Midpoint and
|
01:00 | Let's open a new GeoGebra window. |
01:02 | Click on Dash home Media Apps. |
01:07 | Under Type Choose Education and GeoGebra. |
01:15 | Let's state a theorem |
01:18 | Perpendicular from center of circle to a chord bisects the chord |
01:23 | Perpendicular from 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' |
01:45 | uncheck 'Axes' and |
01:47 | Select 'Grid' |
01:52 | 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 open |
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 |
02:14 | 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'. |
02:36 | Click on "Perpendicular line" tool from tool bar |
02:39 | 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'. |
02:52 | Perpendicular line and Chord 'BC' intersect at a point |
02:57 | Click on “Intersect Two objects” tool, |
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' ... |
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 ... |
03:36 | Click on the points 'C','D', 'A' |
03:42 | angle 'CDA' is '90^0'. |
03:46 | TheTheorem is verified. |
03:50 | Let's Move the point 'C' |
03:52 | 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" 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. |
04:54 | 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' and 'C' on the circumference |
05:09 | Let's draw an arc 'BC' |
05:13 | Click on "Circular Arc with Center between Two points" |
05:18 | Click on the point 'A'B' and 'C' on the circumference
|
05:24 | An Arc 'BC' is drawn |
05:27 | 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" |
05:38 | 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'. |
06:04 | 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' |
06:27 | Click on the "Angle" tool, |
06:29 | Click on points 'B', 'D', 'C' and 'B', 'E', 'C' |
06:40 | We can see that the angles 'BDC' and 'BEC' are equal. |
06:52 | 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 the 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. |
09:26 | 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 out put 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 |
10:07 | 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 http://spoken-tutorial.org/NMEICT-Intro ] |
10:29 | This is Madhuri Ganapathi from IIT Bombay signing off .Thank you for joining |