Difference between revisions of "Geogebra/C3/Relationship-between-Geometric-Figures/English-timed"

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Revision as of 16:42, 23 February 2015

Title of script: Relationship between different Geometric Figures

Author: Madhuri Ganapathi

Keywords: video tutorial

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 incircle.
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 opens 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 pointB.
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 from the tool bar, click on the points A, B, C.
05:48 We see that the two angle bisectors intersect at a 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 incircle 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 incircle 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 incircles 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 summarizes 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

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