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

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 pass 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 from 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