View source for GeoGebra-5.04/C2/Theorems-in-GeoGebra/English

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|| ''' Visual Cue'''
|| ''' Narration'''

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|| '''Slide Number 1 ''' 

'''Title slide ''' 
|| Welcome to the spoken tutorial on '''Theorems in GeoGebra'''. 

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|| '''Slide Number 2''' 

'''Learning Objectives''' 
|| In this tutorial we will state and prove, 

* '''Pythagoras''' theorem and 
* Midpoint theorem using '''Geogebra''' .

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|| '''Slide Number 3''' 

'''System Requirement''' 
|| To record this tutorial, I am using; 

* '''Ubuntu Linux''' OS version 16.04 
* '''GeoGebra''' version 5.0.438.0-d. 
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|| '''Slide Number 4''' 

'''Pre-requisites''' 


'''www.spoken-tutorial.org''' 
|| To follow this tutorial, learner should be familiar with '''GeoGebra interface'''. 


For the prerequisite '''GeoGebra''' tutorials, please visit this website. 
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|| '''Slide Number 5''' 

'''Pythagoras Theorem''' 
 
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. 
|| Let us state the '''Pythagoras '''theorem. 

The square of the hypotenuse is equal to the sum of the squares of the other two sides. 

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|| Cursor on the interface. 
|| I have already opened the '''GeoGebra interface'''. 

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|| Cursor on the '''Graphics view'''. 
|| We will begin with the drawing of a semicircle. 

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|| Click on '''Semicircle through 2 Points''' tool. 

Click two points in the '''Graphics view'''. 
|| Click on the '''Semicircle through 2 Points '''tool. 

Then click to mark two points in the '''Graphics view'''. 

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|| Click on Point tool >> click on the '''semicircle c'''. 
|| Using the '''Point''' we will mark another point '''C''' on the semicircle '''c'''. 

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|| Point to the '''semicircle c'''. 
|| Let us now draw a triangle '''ABC''' using the points on the semicircle '''c'''. 

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|| Click on '''Polygon''' tool >> click points '''A''', '''B''', '''C''' and '''A''' again. 
|| Click on the '''Polygon''' tool and draw triangle '''ABC''' on the semicircle. 

Here we are using semicircle to draw the triangle. 

This is because we need the measure of one angle to be 90 degree. 

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|| Point to the triangle. 
|| Now let us measure the angles of the triangle '''ABC'''. 

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|| Click on '''Angle''' tool >> click inside the triangle 
|| Click on the '''Angle''' tool and click inside the triangle. 

Here angle '''ACB''' is 90 degrees. 

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|| Point to '''Algebra''' view. 

Click on blue dot under '''Conic'''. 
|| Now we will hide the semicircle c. 


In the '''Algebra view''' under '''Conic,''' click on the blue dot against '''c'''. 

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|| Point to the sides of the triangle. 
|| We will draw three squares using the sides of the triangle. 

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|| Click on '''Regular Polygon''' tool >> click on the points '''C''' and '''B'''. 
|| For that click on the '''Regular Polygon''' tool and then click on the points '''C''', '''B'''. 

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|| Point to the dialog box and value 4. 


Click on '''OK''' button at the bottom. 
|| The '''Regular Polygon''' text box opens with a default value 4. 


Click on '''OK''' button at the bottom. 

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|| Click on points '''B''', '''C'''. 
|| If you click on the points '''B''', '''C''', the square is drawn in the opposite direction. 

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|| Click on '''Undo''' button on the top right corner of the toolbar. 
|| Let us undo the process by clicking on the '''Undo''' button. 

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|| Click on points '''A''', '''C''' >> click button in '''Regular Polygon''' text box. 
|| Now click on the points '''A''', C'''. 


And then click the '''OK''' button in the text box that appears. 

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|| Click on points '''B''', '''A'''  >> click button in '''Regular Polygon''' text box. 
|| Similarly click on the points '''B''', '''A'''. 

And then click the '''OK''' button in the text box that appears. 

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|| Point to the three squares. 
|| Now we have three squares that represent the '''Pythagorean triplets'''. 

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|| Click on '''Zoom Out''' tool >> click on the diagram. 
|| Now we will use '''Zoom Out''' tool to see the diagram clearly. 

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|| Point to the three squares. 
|| Now we will find the area of these squares. 

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|| Click on '''Area''' tool >> click on '''poly1''' >> click on '''poly2''' >> click on '''poly3'''. 


Point to the areas. 
|| Click on the '''Area''' tool and click on '''poly1''', '''poly2''' and '''poly3''' respectively. 


The areas of the respective squares are displayed. 

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|| Click on '''Move''' tool >> drag the labels. 
|| Using the '''Move''' tool drag the labels to see them clearly. 

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|| Point to the areas of the squares. 
|| Now we will check if the area of '''poly1''' + area of '''poly 2''' is equal to area of '''poly3.''' 

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|| In the input bar type '''poly1 + poly2 ''' >> press '''Enter'''. 


Point to''' Algebra view.''' 
|| In the '''input bar ''' type '''poly1+ poly2 ''' and press '''Enter'''. 


In the Algebra view a '''Number d''',  shows the value of area of '''poly3'''. 

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|| Point to the figure. 
|| Hence '''Pythagoras''' theorem has been proved. 

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|| Point to the figure. 
|| Now I will explain the '''Construction Protocol''' for '''pythagoras''' theorem. 


'''Construction Protocol''' shows the step by step construction of the diagram as an animation. 

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|| Click on '''View''' menu >> select '''Construction Protocol''' check box. 


Point to the view. 
|| To view the animation, click on '''View''' menu and select '''Construction Protocol''' check box. 


'''Construction Protocol view''' opens next to '''Graphics view'''. 

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|| 
|| I will drag the boundary of Graphics view view to see the '''Construction Protocol view'''. 

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|| Point to the columns in the table. 
|| This view has a table with some columns. 


Below the table we have the animation controls. 

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|| Click on '''Play''' button. 


Point to the animation. 
|| Now click on the '''Play''' button. 


Watch the step by step construction of the figure as an animation. 

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|| '''Slide Number 6''' 

'''Mid point Theorem''' 


Line segment joining the mid-points of two sides of a triangle is parallel to the third side and half of it. 
|| Next we will prove the Mid-point theorem. 


The line segment joining the mid-points of two sides of a triangle is parallel to the third side and half of it. 

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|| Cursor on the interface.
|| I have opened a new '''GeoGebra''' window. 

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|| Click on '''Polygon''' tool >> click on the points '''A''', '''B''', '''C''', '''D''' and '''A''' again. 
|| Let us draw a triangle '''ABC''' using '''Polygon''' tool. 
 
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|| Point to the sides '''AB''' and '''AC'''. 
|| Now we will find the mid-points of the sides '''AB''' and '''AC'''. 

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|| Click on the '''Midpoint or Center ''' tool. 

Click on sides '''AB''' and '''AC'''. 
|| Click on the '''Midpoint or Center''' tool. 

Then click on the sides '''AB''' and '''AC'''. 

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|| Click on '''Line''' tool >> click on points '''D''' and '''E'''. 
|| Using the '''Line''' tool, draw a line through points '''D''' and '''E'''. 

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|| Point to the line '''AB'''. 
|| Now we will draw a line parallel to segment '''AB'''. 

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|| Click on the '''Parallel Line''' tool >> click on segment '''AB'''. 


Click on point '''C'''. 


Point to the line. 
|| For this, click on the '''Parallel Line''' tool and click on segment '''AB'''. 


Then, click on point '''C'''. 


Line '''g''' parallel to segment '''AB''' is drawn. 

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|| Point to the intersection point. 
|| Notice that lines '''f''' and '''g''' intersect at a point. 

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|| Click on '''Intersect''' tool >> click on point of intersection. 
|| Using the '''Intersect''' tool, let us mark the point of intersection as '''F'''. 

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|| Click on '''Angle''' tool >> click on the points '''F''', '''C''', '''E''' and '''D''', '''A''', '''E'''. 
|| Now we need to measure angles '''F C E''' and '''D A E'''. 

Click on the '''Angle''' tool and click on the points  '''F''', '''C''', '''E''' and '''D''', '''A''', '''E'''. 

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|| Point to the angles. 
|| Notice that angles are equal since they are alternate interior angles. 

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|| Click on '''Angle''' tool >> click on the points '''C''', '''B''', '''D''' and '''E''', '''D''', '''A'''. 

Point to the line f and segment '''BC. '''
|| Similarly we will measure '''C''', '''B''', '''D''' and '''E''', '''D''', '''A''' .


The angles are equal. 


It implies that line '''f''' is parallel to segment '''BC'''. 

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|| Click on '''Distance or Length''' tool >> click on points '''D''', '''E''' and '''B''', '''C'''. 


Point '''DE''' and '''BC'''. 
|| Using the '''Distance or Length''' tool, 

click on the points '''D''', '''E''' and '''B''', '''C'''. 


Notice that '''DE''' is half of '''BC'''. 

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|| Point to the figure. 
|| Hence the mid-point theorem is proved. 

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|| Point to the figure. 
|| Once again I will show the '''Construction Protocol''' for the theorem. 

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|| Click on '''View '''menu >> select '''Construction Protocol '''check box. 


Point to the view. 
|| Click on '''View''' menu and select '''Construction Protocol''' check box. 


'''Construction Protocol''' view opens next to '''Graphics view'''. 

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|| Click on '''Play''' button. 


Point to the animation. 
|| Now click on the '''Play''' button. 

Watch the step by step construction of the figure. 

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|| '''Slide Number 7''' 

'''Assignment''' 


'''In a right triangle, the altitude is the geometric mean of the two segments of the hypotenuse'''. 
|| As an assignment, prove this theorem. 

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|| Point to the figure. 
|| Your completed assignment should look like this. 

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|| 
|| Let us summarize what we have learnt. 

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|| '''Slide Number 8''' 

summary 
|| In this tutorial we stated and proved, 

* '''Pythagoras''' theorem and 
* Midpoint theorem using '''Geogebra''' 

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|| '''Slide Number 9''' 

'''About Spoken Tutorial project''' 
|| The video at the following link summarizes the Spoken Tutorial project. 

Please download and watch it. 

|- 
|| '''Slide Number 10''' 

'''Spoken Tutorial workshops''' 
|| The '''Spoken Tutorial Project '''team conducts workshops and gives certificates. 

For more details, please write to us. 

|- 
|| '''Slide Number 11''' 

'''Forum for specific questions:''' 

* Do you have questions in THIS '''Spoken Tutorial'''? 
* Please visit this site 
* Choose the minute and second where you have the question. 
* Explain your question briefly 
* Someone from our team will answer them. 

|| Please post your timed queries in this forum. 
 
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|| '''Slide Number 12''' 

'''Acknowledgement''' 
|| Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India. 

More information on this mission is available at this link. 

|- 
|| 
|| This is Madhuri Ganapathi from, IIT Bombay signing off. 

Thank you for watching. 
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