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

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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.

Contributors and Content Editors

PoojaMoolya