GeoGebra-5.04/C2/Theorems-in-GeoGebra/English-timed
From Script | Spoken-Tutorial
| 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 5.0.438.0-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. |
