GeoGebra-5.04/C2/Theorems-in-GeoGebra/English-timed

Time	Narration
00:01	Welcome to the spoken tutorial on Theorems in GeoGebra.
00:06	In this tutorial we will state and prove, Pythagoras theorem and Midpoint theorem using Geogebra .
00:16	To record this tutorial, I am using; Ubuntu Linux OS version 16.04 GeoGebra version 5.0438.0-d.
00:29	To follow this tutorial, learner should be familiar with GeoGebra interface. For the prerequisite GeoGebra tutorials, please visit this website.
00:40	Let us state the Pythagoras theorem.
00:43	The square of the hypotenuse (the side opposite to the right angle) is equal to the sum of the squares of the other two sides.
00:50	I have already opened the GeoGebra interface.
00:54	We will begin with the drawing of a semicircle.
00:58	Click on the Semicircle through 2 Points tool.
01:02	Then click to mark two points in the Graphics view.
01:07	Using the Point we will mark another point C on the semicircle c.
01:14	Now let us draw a triangle ABC using the points on the semicircle.
01:19	Click on the Polygon tool and draw triangle ABC
01:26	Here we are using semicircle to draw the triangle.
01:30	This is because we need the measure of one angle to be 90 degree.
01:36	Let us measure the angles of the triangle.
01:39	Click on the Angle tool and click inside the triangle. Here angle ACB is 90 degrees.
01:49	Now we will hide the semicircle c.
01:52	In the Algebra view under Conic, click on the blue dot against c.
01:58	We will draw three squares using the sides of the triangle.
02:02	For that click on the Regular Polygon tool and then click on the points C, B.
02:09	The Regular Polygon text box opens with a default value 4.
02:14	Click on OK button at the bottom.
02:17	If you click on the points B, C, the square is drawn in the opposite direction.
02:25	Let us undo the process by clicking on the Undo button.
02:29	Now click on the points A, C. And then click the OK button in the text box that appears.
02:37	Similarly click on the points B, A. And then click the OK button in the text box that appears.
02:46	Now we have three squares that represent the Pythagorean triplets.
02:51	Now we will use Zoom Out tool to see the diagram clearly.
02:57	Now we will find the area of these squares.
03:01	Click on the Area tool and click on poly1, poly2 and poly3 respectively.
03:12	The areas of the respective squares are displayed.
03:16	Using the Move tool drag the labels to see them clearly.
03:29	Now we will check if the area of poly1 + area of poly 2 is equal to area of poly3.
03:36	In the input bar type poly1+ poly2 and press Enter.
03:43	In the Algebra view a Number d, shows the value of area of poly3.
03:49	Hence Pythagoras theorem has been proved.
03:52	Now I will explain the Construction Protocol for pythagoras theorem.
03:57	Construction Protocol shows the step by step construction of the diagram as an animation.
04:03	To view the animation, click on View menu and select Construction Protocol check box.
04:10	Construction Protocol view opens next to Graphics view.
04:15	I will drag the boundary of Graphics view view to see the Construction Protocol view.
04:21	This view has a table with some columns. Below the table we have the animation controls.
04:29	Now click on the Play button.
04:32	Watch the step by step construction of the figure as an animation.
04:50	Now we will prove the Mid-point theorem.
04:53	The line segment joining the mid-points of two sides of a triangle is parallel to the third side and half of it.
05:01	I have opened a new GeoGebra window.
05:05	Let us draw a triangle ABC using Polygon tool.
05:16	Now we will find the mid-points of the sides AB and AC.
05:21	Click on the Midpoint or Center tool. Then click on the sides AB and AC.
05:30	Using the Line tool, draw a line through points D and E.
05:38	Now we will draw a line parallel to segment AB.
05:42	For this, click on the Parallel Line tool and click on segment AB.
05:49	Then, click on point C. Line g parallel to segment AB is drawn.
05:56	Notice that lines f and g intersect at a point.
06:01	Using the Intersect tool, let us mark the point of intersection as F.
06:08	Now we need to measure angles F C E and D A E.
06:17	Click on the Angle tool and click on the points F, C, E and D, A, E.
06:32	Notice that angles are equal since they are alternate interior angles.
06:38	Similarly we will measure C, B, D and E, D, A .
06:49	The angles are equal. This implies that line f is parallel to segment BC.
06:56	Using the Distance or Length tool, click on the points D, E and B, C. Notice that DE is half of BC.
07:09	Hence the mid-point theorem is proved.
07:12	Once again I will show the Construction Protocol for the theorem.
07:17	Click on View menu select Construction Protocol check box.
07:23	Construction Protocol' view opens next to Graphics view.
07:28	Now click on the Play button. Watch the step by step construction of the figure.
07:51	As an assignment, prove this theorem.
07:55	Your completed assignment should look like this.
07:59	Let us summarize what we have learnt.
08:02	In this tutorial we stated and proved, Pythagoras theorem and Midpoint theorem using Geogebra
08:12	The video at the following link summarizes the Spoken Tutorial project. Please download and watch it.
08:20	The Spoken Tutorial Project team conducts workshops and gives certificates. For more details, please write to us.
08:28	Please post your timed queries in this forum.
08:32	Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India. More information on this mission is available at this link.
08:43	This is Madhuri Ganapathi from, IIT Bombay signing off. Thank you for watching.

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