Geogebra/C3/Relationship-between-Geometric-Figures/English-timed

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Title of script: Relationship between different Geometric Figures

Author: Madhuri Ganapathi

Keywords: video tutorial

Click here for Slides

Time Narration
00:00 Hello.
00:01 And welcome to the spoken tutorial on Relationship between different Geometric Figures in Geogebra
00:07 We assume that you have the basic working knowledge of Geogebra.
00:11 If not, please go through the “Introduction to Geogebra” tutorial before proceeding further.
00:18 Please note that the intention to teach this tutorial is not to replace the actual compass box.
00:24 Construction in GeoGebra is done with the view to understand the properties.
00:29 In this tutorial we will learn to construct


00:32 Cyclic quadrilateral and In-circle
00:35 To record this tutorial I am using

Linux operating system

00:39 Ubuntu Version 10.04 LTS
00:43 And Geogebra Version 3.2.40.0
00:48 We will use the following Geogebra tools for the construction
  • compass
  • segment between two points
  • circle with center through point
  • polygon
  • perpendicular bisector
  • angle bisector and
  • angle
01:02 Let us switch on to the Geogebra window.
01:05 To do this let us click on applications, Education and Geogebra.


01:13 Let me resize this window.
01:18 Click on the options menu click on font size and then on 18 point to make the figure clear.


01:25 Let us construct a cyclic quadrilateral.
01:27 To do this let us select the "Regular Polygon" tool from the tool bar click on the "Regular Polygon" tool click on any two points on the drawing pad.
01:38 We see that a dialog box open with a default value '4'.
01:42 click OK.


01:43 A square 'ABCD' is drawn.


01:46 Let's tilt the square Using the “Move” tool which is at the left corner.
01:51 Select the "Move" tool from the tool bar, click on the Move tool
01:56 Place, the mouse pointer on 'A' or on 'B'. I will choose B
02:01 Place the mouse pointer on B and drag it with the mouse. We see that the square is in the tilted position now.
02:10 Let's construct a perpendicular bisector to the segment 'AB'.
02:15 To do this Let's Select “Perpendicular bisector” tool from the tool bar.
02:20 Click on the "Perpendicular bisector" tool.
02:22 click on the point 'A'
02:24 and then on point'B'
02:26 We see that a "Perpendicular bisector" is drawn.
02:30 Let's construct a second perpendicular bisector to segment 'BC' to do this
02:36 Select “perpendicular bisector” tool from the tool bar, click on the “perpendicular bisector” tool.
02:42 click on the point 'B'
02:44 and then on point 'C'
02:46 We see that the perpendicular bisectors intersect at a point .
02:50 Let us mark this point as 'E'
02:54 Let's now construct a circle with centre as 'E' and which passes through C .
03:01 Let's select the "circle with centre through point" tool from tool bar click on the "circle with centre through point" tool.
03:09 Click on point 'E' as centre and which passes through 'C'. Click on the point 'E' and then on point 'C'.
03:18 We see that the circle will passes through all the vertices of the quadrilateral.A Cyclic Quadrilateral is drawn.
03:29 Do you know , that the cyclic quadrilateral has maximum area among all the quadrilaterals of the same sequence of side lengths.
03:37 Let's use the "Move" tool, to animate the figure.
03:42 To do this Let's select the "Move" tool from the tool bar, click on the "Move" tool place the mouse pointer on 'A' or 'B'. I will choose 'A'.
03:52 Place the mouse pointer on 'A' and drag it with the mouse to animate.
03:58 To verify that the construction is correct.
04:01 Let's now save the file.
04:04 Click on "File" "Save As".
04:07 I will type the file name as "cyclic_quadrilateral"
04:21 and click on save
04:23 Let us now open a new geogebra window to construct an incircle.
04:28 To do this Let's select on File and New.
04:35 Let's now construct a triangle to do this , Let's select the "Polygon" tool from the tool bar, Click on the "Polygon" tool.
04:44 click on the points A,B,C and A once again to complete the triangle figure.
04:52 Let's measure the angles for this triangle,
04:55 To do this Let's select the "Angle" tool from the tool bar, click on the Angle tool.


05:00 Click on the points 'B,A,C' , 'C,B,A' and 'A,C,B'.
05:15 We see that the angles are measured.
05:18 Lets now construct angle bisectors to these angles.
05:21 Select the "Angle bisector" tool from the tool bar,
05:25 click on the "Angle bisector" tool.Click on the points 'B,A,C' .
05:32 Let's select the "Angle bisector" tool again from the tool bar to construct second angle bisector.
05:39 click on the "Angle bisector" tool and the tool bar, click on the points A,B,C.
05:48 We see that the two angle bisectors intersect at point .
05:52 Let's mark this point as 'D'.
05:55 Let's now construct a perpendicular line which passes through point D and segment AB.
06:02 Select “perpendicular line” tool from tool bar,click on the “perpendicular line” tool, click on the point D and then on segment AB.
06:12 We see that the perpendicular line intersects segment AB at a point.
06:17 Let's mark this point as 'E'.
06:20 Let's now construct a circle with centre as D and which passes through 'E'.
06:27 Let's select the "compass" tool from tool bar , click on the "compass" tool,click on the point D as centre and DE as radius.
06:37 Click on the point 'D' and then on point 'E' and 'D' once again to complete the figure.
06:46 We see that the circle touches all the sides of the triangle.
06:50 An in-circle is drawn.
06:53 With this we come to an end of this tutorial.


06:57 To Summarize
07:02 In this tutorial we have learnt to construct
07:05 cyclic quadrilateral and
07:07 In-circle using the Geogebra tools.
07:10 As an assignment i would like you to draw a triangle ABC
07:15 Mark a point D on BC, join AD
07:19 Draw in-circles form triangles ABC, ABD and CBD of radii r, r1 and r2 .
07:28 BE is the height h
07:30 Move the vertices of the Triangle ABC
07:33 To verify the relation.
07:35 (1 -2r1/h)*(1 - 2r2/h) = (1 -2r/h)
07:43 The output of the assignment should look like this.
07:52 Watch the video available at this URL.
07:55 It summarises the Spoken Tutorial project.
07:57 If you do not have good bandwidth, you can download

and watch it

08:02 The Spoken Tutorial Project Team :Conducts workshops using spoken tutorials.
08:06 Gives certificates to those who pass an online test
08:09 For more details, contact us contact@spoken-tutorial.org
08:16 Spoken Tutorial Project is a part of Talk to a Teacher project
08:19 It is supported by the National Mission on Education through ICT, MHRD, Government of India.
08:25 More information on this Mission is available at this link.
08:29 This is Madhuri Ganapathi from IIT Bombay signing off

Thanks for joining.

Contributors and Content Editors

Madhurig, Minal, Nancyvarkey, PoojaMoolya, Pratik kamble, Sandhya.np14