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

From Script | Spoken-Tutorial
Jump to: navigation, search
 
(3 intermediate revisions by 2 users not shown)
Line 7: Line 7:
 
|-
 
|-
 
||00:08
 
||00:08
−
||At the end of this  tutorial,  
+
||At the end of this  tutorial, you will be able to  verify theorems on:  
−
 
+
−
|-
+
−
||00:09
+
−
||you will be able to  verify theorems on:  
+
  
 
|-
 
|-
Line 45: Line 41:
 
|-
 
|-
 
||00:47
 
||00:47
−
||* Circle with Center and Radius  
+
||Circle with Center and Radius  
  
 
|-
 
|-
 
||00:49
 
||00:49
−
||* Circular Sector with Center between Two Points
+
||Circular Sector with Center between Two Points
  
 
|-
 
|-
 
||00:53
 
||00:53
−
||* Circular Arc with Center between Two points
+
||Circular Arc with Center between Two points
  
 
|-
 
|-
 
||00:56
 
||00:56
−
||* Midpoint  and
+
||Midpoint  and
  
 
|-
 
|-
 
||00:58
 
||00:58
−
||* Perpendicular line  
+
||Perpendicular line  
 
|-
 
|-
 
||01:00
 
||01:00
Line 105: Line 101:
 
||01:47
 
||01:47
 
||Select '''Grid'''.
 
||Select '''Grid'''.
 +
 
|-
 
|-
 
||01:51
 
||01:51
Line 118: Line 115:
 
|-
 
|-
 
||02:01
 
||02:01
−
||A dialogue box opens.
+
||A dialog box opens.
 
|-
 
|-
 
||02:03
 
||02:03
Line 125: Line 122:
 
|-
 
|-
 
||02:06
 
||02:06
−
||Click '''OK'''.
+
||Click '''OK'''. A circle with center '''A''' and radius '''3cm''' is drawn.
−
|-
+
−
||02:07
+
−
||A circle with center '''A''' and radius '''3cm''' is drawn.
+
  
 
|-
 
|-
Line 205: Line 199:
 
|-
 
|-
 
||03:42
 
||03:42
−
|| angle '''CDA''' is '90' degrees.
+
||angle '''CDA''' is '90' degrees.
  
 
|-
 
|-
Line 409: Line 403:
 
|-
 
|-
 
||08:57
 
||08:57
−
||*  Perpendicular  from center to a  chord bisects it  
+
||Perpendicular  from center to a  chord bisects it  
  
 
|-
 
|-
 
||09:00
 
||09:00
−
||*  Inscribed angles subtended by the same  arc  are equal  
+
||Inscribed angles subtended by the same  arc  are equal  
  
 
|-
 
|-
 
||09:06
 
||09:06
−
||* 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.
  
 
|-
 
|-
Line 429: Line 423:
 
|-
 
|-
 
||09:24
 
||09:24
−
||Draw a circle.  
+
||Draw a circle. Select Segment with given length from point tool.  
−
 
+
−
|-
+
−
||09:25
+
−
||Select Segment with given length from point tool.  
+
  
 
|-
 
|-

Latest revision as of 14:48, 28 October 2020

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, 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 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, 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 dialog box opens.
02:03 Let's type value 3 for radius.
02:06 Click OK. 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 The theorem 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's open a new Geogebra window.
04:51 Click on File >> New.
04:55 Let's draw a circle.
04:57 Click on 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 points 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 measure the 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 the 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. 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 summarizes 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=54169"