Geogebra/C3/Theorems-on-Chords-and-Arcs/English-timed
From Script | Spoken-Tutorial
| Visual Cue | 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 now verify the 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 |
