Difference between revisions of "GeoGebra-5.04/C2/Basics-of-Triangles/English"

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(Created page with "{|border=1 ||'''Visual Cue''' ||'''Narration''' |- ||'''Slide Number 1 ''' '''Title slide ''' || Welcome to this Spoken tutorial on '''Basics of Triangles''' in '''GeoGebr...")
 
 
(One intermediate revision by one other user not shown)
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|| To record this tutorial, I am using;  
 
|| To record this tutorial, I am using;  
  
−
Ubuntu Linux OS version 14.04  
+
*'''Ubuntu Linux''' OS version 14.04  
  
−
GeoGebra version 5.0438.0-d  
+
*'''GeoGebra''' version 5.0.438.0-d  
  
 
|-  
 
|-  
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|-  
 
|-  
 
||Point to the icons.  
 
||Point to the icons.  
−
|| Before I begin, I will increase the '''font''' size to show the icons clearly.  
+
|| Before I begin, I will increase the '''font size''' to show the icons clearly.  
  
 
|-  
 
|-  
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Right-click on the '''Graphics view.'''  
 
Right-click on the '''Graphics view.'''  
  
−
And from the '''Graphics''' menu, uncheck '''Axes'''.  
+
And from the '''Graphics''' menu, uncheck the '''Axes'''.  
  
 
|-  
 
|-  
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|| Click on '''Polygon''' tool.  
 
|| Click on '''Polygon''' tool.  
  
−
Click on the '''Graphics view''' to draw three vertices '''A''', '''B''' and '''C'''.  
+
Click on the '''Graphics view''' to draw three vertices '''A, B''' and '''C'''.  
  
  
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* Lengths of the sides and  
 
* Lengths of the sides and  
 
* Area of the triangle.  
 
* Area of the triangle.  
 +
 
|-  
 
|-  
 
|| Point to the triangle.
 
|| Point to the triangle.
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−
Click the vertices '''BAC''', '''CBA ''', '''ACB'''.  
+
Click the vertices '''B A C, C B A, A C B'''.  
  
 
|-  
 
|-  
 
||Point to the values in '''Algebra view'''.  
 
||Point to the values in '''Algebra view'''.  
−
|| Values of the angles '''alpha''', '''beta''' and '''gamma''' are displayed in the '''Algebra view'''.  
+
|| Values of the angles '''alpha, beta''' and '''gamma''' are displayed in the '''Algebra view'''.  
  
 
|-  
 
|-  
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|-  
 
|-  
 
||Point to the triangle.  
 
||Point to the triangle.  
−
|| Next let us display the perimeter and area of the triangle.  
+
|| Let us display the perimeter and area of the triangle.  
  
 
|-  
 
|-  
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point '''Symbols''' and '''Objects''' drop-downs.  
 
point '''Symbols''' and '''Objects''' drop-downs.  
−
|| The text tool has,  
+
|| The '''Text''' tool has,  
  
 
* An '''Edit''' box to type text  
 
* An '''Edit''' box to type text  
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Type,  
 
Type,  
  
−
'''Sum of Angles = '''select '''alpha''' from '''Objects '''drop-down '''+''' select '''beta''' from''' Objects''' drop-down '''+''' select '''gamma''' from '''Objects''' drop-down '''<nowiki>= </nowiki>'''select '''delta '''from '''Objects''' drop-down.
+
'''Sum of Angles = '''
 
|| In the '''Edit''' text box type,  
 
|| In the '''Edit''' text box type,  
  
−
'''Sum of the Angles <nowiki>= </nowiki>'''select '''alpha''' from '''Objects '''drop-down '''+''' select '''beta''' from''' Objects''' drop-down '''+''' select '''gamma''' from '''Objects''' drop-down '''<nowiki>= </nowiki>'''select '''delta '''from '''Objects''' drop-down.  
+
'''Sum of the Angles <nowiki>= </nowiki>'''
 +
 
 +
|-
 +
||select '''alpha''' from '''Objects '''drop-down '''+''' select '''beta''' from''' Objects''' drop-down '''+''' select '''gamma''' from '''Objects''' drop-down '''<nowiki>= </nowiki>'''select '''delta '''from '''Objects''' drop-down.
 +
||Select '''alpha''' from '''Objects '''drop-down '''+''' select '''beta''' from''' Objects''' drop-down '''+''' select '''gamma''' from '''Objects''' drop-down '''<nowiki>= </nowiki>'''select '''delta '''from '''Objects''' drop-down.  
  
 
|-  
 
|-  
 
||Point to the values in the '''Preveiw '''box.  
 
||Point to the values in the '''Preveiw '''box.  
−
|| Observe the entered text and the values of selected angles in the '''Preview''' box.  
+
|| Observe the entered text and the values of the selected angles in the '''Preview''' box.  
  
 
|-  
 
|-  
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Click on''' Angle '''tool >> click the points '''DCA'''.  
 
Click on''' Angle '''tool >> click the points '''DCA'''.  
−
|| Now we will measure the exterior angle of triangle '''ABC'''.  
+
|| Now we will measure the exterior angle of the triangle '''ABC'''.  
  
  
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Open parenthesis.  
 
Open parenthesis.  
  
−
Inside parenthesis,  
+
Inside parentheses, select '''alpha''' from symbols table.
  
−
select '''alpha''' from symbols table,
+
Press plus sign on the keyboard,  
−
 
+
−
press plus sign on the keyboard,  
+
  
 
select '''beta'''.  
 
select '''beta'''.  
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−
Inside the parenthesis, select '''alpha''' from the '''symbols table'''.  
+
Inside the parentheses, select '''alpha''' from the '''symbols table'''.  
  
  
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* Draw a triangle and measure its angles.  
 
* Draw a triangle and measure its angles.  
  
−
* Measure area and perimeter of the triangle  
+
* Display perimeter and area of the triangle  
  
−
* Show that, the sum of the angles of a triangle is 180 degrees  
+
* Show that sum of the angles of a triangle is 180 degrees  
  
 
* Show that, exterior angle is equal to sum of the interior opposite angles.  
 
* Show that, exterior angle is equal to sum of the interior opposite angles.  
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* Altitudes of the triangle and located the orthocenter.  
 
* Altitudes of the triangle and located the orthocenter.  
  
−
* incircle to a triangle.  
+
* An incircle to a triangle.  
 
|-  
 
|-  
 
||'''Slide Number 8'''  
 
||'''Slide Number 8'''  
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−
Draw a '''circumscribed circle''' to the triangle.  
+
*Draw a '''circumscribed circle''' to the triangle.  
  
−
 
+
*Hint: Draw perpendicular bisectors to the sides of the triangle.  
−
Hint: Draw perpendicular bisectors to the sides of the triangle.  
+
  
 
|-  
 
|-  
 
||Show the Assignment.  
 
||Show the Assignment.  
−
|| Your assignment should look like this  
+
|| Your assignment should look like this.
  
 
|-  
 
|-  
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−
Draw '''medians''' to the triangle.  
+
*Draw '''medians''' to the triangle.  
  
−
Mark the intersection point of''' medians'''  
+
*Mark the intersection point of''' medians'''.
  
−
Rename the point as '''centroid.'''  
+
*Rename the point as '''centroid.'''  
  
 +
*Hint: Mark midpoints of the sides.
  
−
Hint: Mark midpoints of the sides
+
*Join the midpoint of each side with the opposite vertex.  
−
 
+
−
Join the midpoint of each side with the opposite vertex.  
+
  
 
|-  
 
|-  
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'''Spoken Tutorial workshops'''  
 
'''Spoken Tutorial workshops'''  
−
|| The '''Spoken Tutorial Project '''team:
+
|| The '''Spoken Tutorial Project '''team conducts workshops and gives certificates.  
−
 
+
−
conducts workshops and  
+
−
 
+
−
* gives certificates.  
+
  
 
For more details, please write to us.  
 
For more details, please write to us.  

Latest revision as of 14:44, 10 October 2019

Visual Cue Narration
Slide Number 1

Title slide

Welcome to this Spoken tutorial on Basics of Triangles in GeoGebra.
Slide Number 2

Learning Objectives

In this tutorial we will, learn to
  • Draw a triangle and measure its angles
  • Display perimeter and area of the triangle
  • Show that sum of the angles of a triangle is 180 degrees
  • Show that exterior angle is equal to sum of the interior opposite angles
Slide Number 3

Learning Objectives

Also we will learn to draw,
  • Altitudes of the triangle and locate the orthocenter
  • An incircle to a triangle.
Slide Number 4

System Requirement

To record this tutorial, I am using;
  • Ubuntu Linux OS version 14.04
  • GeoGebra version 5.0.438.0-d
Slide Number 5

Pre-requisites


www.spoken-tutorial.org

To follow this tutorial, learner should be familiar

with Geogebra interface.


If not for relevant GeoGebra tutorials please visit our webiste.

Cursor on the GeoGebra window. I have opened a new GeoGebra window.
Point to the icons. Before I begin, I will increase the font size to show the icons clearly.
Go to Options menu >> select Font Size.

From the sub-menu select 18 pt radio button.

Go to Options menu and select Font Size.


From the sub-menu select 18 pt radio button.

Right-click on the Graphics view.

From Graphics menu, uncheck Axes.

For this tutorial I will uncheck the Axes.


Right-click on the Graphics view.

And from the Graphics menu, uncheck the Axes.

Cursor on the GeoGebra window. Now we will draw a triangle ABC.
Click on Polygon tool>> click on Graphics view>>click on Points A, B, C and A again. Click on Polygon tool.

Click on the Graphics view to draw three vertices A, B and C.


Then click on vertex A again to complete the triangle.

Point to the values in the Algebra view. As we draw the triangle, observe the corresponding values in the Algebra view.

It displays:

  • Coordinates of vertices
  • Lengths of the sides and
  • Area of the triangle.
Point to the triangle. Now let us learn to measure the angles of the triangle.
Click on Angle tool.

Click the vertices BAC, CBA , ACB.

Click on the Angle tool.


Click the vertices B A C, C B A, A C B.

Point to the values in Algebra view. Values of the angles alpha, beta and gamma are displayed in the Algebra view.
Cursor on the overlapping labels. Now we will move the overlapping labels.
Click on Move tool>> drag the labels. Click on the Move tool and drag the labels to see them clearly.
Point to the triangle. Let us display the perimeter and area of the triangle.
Click on Angle tool drop-down >> select Distance or Length tool. Click on the Angle tool drop-down and select the Distance or Length tool.
Click on the triangle ABC.

Perimeter of triangle ABC is displayed on the triangle.

Click on the triangle ABC.

Perimeter of triangle is displayed on the triangle.

Click on Angle tool drop-down >> select Area tool >> click on the triangle ABC.

Point to the displayed area.

Now select the Area tool and click on the triangle ABC to display it.
Cursor on the Triangle ABC. Next we will find the sum of the angles of the triangle ABC using the input bar.
In the Input bar,

(select alpha+select beta+select gamma)

Press Enter.

In the input bar, open parentheses.

Inside the parentheses, select alpha from the symbols table.

Now type plus sign, select beta.


Once again type plus sign and select gamma.

Press Enter.

Point to delta value in the Algebra view. Observe the value of angle delta in the Algebra view.

It is equal to 180 degree.

Click on Text tool >> click on Graphics view.


Point to Text tool appears.

Now click on the Slider drop-down and select the Text tool.


Then click on the Graphics view.


A text window opens on the Graphics view.

Point to Edit box.

Point to Preview box.

Point to Latex formula check-box

point Symbols and Objects drop-downs.

The Text tool has,
  • An Edit box to type text
  • A Preview box to show the preview of the typed text
  • A Latex formula check box
  • Symbols drop-downs and
  • Objects drop-down.
Point to the triangle ABC. Now we will show that, the sum of the angles of the triangle is 180 degrees.
Point to the Edit text box.

Type,

Sum of Angles =

In the Edit text box type,

Sum of the Angles =

select alpha from Objects drop-down + select beta from Objects drop-down + select gamma from Objects drop-down = select delta from Objects drop-down. Select alpha from Objects drop-down + select beta from Objects drop-down + select gamma from Objects drop-down = select delta from Objects drop-down.
Point to the values in the Preveiw box. Observe the entered text and the values of the selected angles in the Preview box.
Click on OK button. Click on the OK button at the bottom.
Point to the Graphics view. The text will be displayed on the Graphics view.
Click on Move tool >> drag point A, B or C. Using the Move tool drag the points A, B or C.


Observe that, the sum of the angles of the triangle always shows 180 degrees.

Point to segment BC.


Click on Line tool >> click on points B and C.

Now we will draw a line extending segment BC.


Click on the Line tool, then click on points B and C.

Click on Point tool> click next to C. Using the Point tool we will mark a point D on line f next to C.
Point to triangle ABC.


Click on Angle tool >> click the points DCA.

Now we will measure the exterior angle of the triangle ABC.


Click on the Angle tool and then click on the points DCA.

Click on Move tool drag the labels of the angles and point. Using the Move tool, drag the overlapping labels of the angles and points.
Point to angle epsilon in Graphics veiw . We will now learn to change the colour of angle epsilon.
Right-click on angle epsilon.

From the sub-menu select Object Properties.

Right-click on angle epsilon.

From the sub-menu, select Object Properties.

Preferences window opens. Preferences window opens.
Click on Color tab >> choose colour to Maroon >> drag Opacity slider. In the Color tab change the colour to Maroon and drag the Opacity slider.
Click on X button to close. Close the Preferences window.
Point to angle epsilon. Now we will check if exterior angle is equal to sum of interior opposite angles.
Point to input bar.

Open parenthesis.

Inside parentheses, select alpha from symbols table.

Press plus sign on the keyboard,

select beta.

Press Enter.

In the input bar, open the parentheses.


Inside the parentheses, select alpha from the symbols table.


Then press the plus sign on the keyboard and select beta.


Press Enter.

Point to Algebra view.

Point to epsilon and delta.


Point to alpha and beta.

Observe - in the Algebra view a new angle tau equal to epsilon is created.


Angle tau is the sum of the angles alpha and beta.

Drag point C.


See the changes in the Algebra and Graphics views.

Using the Move tool drag point C and observe the changes.

We see that angle epsilon is equal to angle tau.

Click on Polygon tool to draw triangle ABC.


Click on Angle tool to measure the angles(BAC, CBA, ACB)

Next I will open a new window with triangle ABC and angles already drawn.
Cursor on triangle ABC. Then we will draw altitudes and an orthocentre to the triangle ABC.
Point to the sides of the traingle. For this we will first draw external lines on all the sides of triangle ABC.
Click on Line tool >> click on points A, B. Click the Line tool then click on points A, B.
click on points B, C and A, C. Similarly click on points B, C and A, C.
Point to the triangle. Now we will draw altitudes to the triangle ABC.
Click on Perpendicular line tool.

Click on point A and line g

Click on the Perpendicular Line tool.

Click on point A and line g.

click on point B and line h.

Click on point C and line f.

Similarly click on point B and line h.

Click on point C and line f.

Point to the intersection. The three altitudes of the triangle meet at a point.
Click on intersect >> mark the point of intersection as D.


Point to D.

Click on the Intersect tool and mark the point of intersection as D.


Point D is the orthocenter of the triangle ABC.

Right-click on point D.

From the sub-menu select Rename.

Let us rename point D as orthocenter.


Right-click on point D.

From the sub-menu select Rename.

Point to Rename text box.

Type Orthocenter.

Click on OK button at the bottom.

Rename text box opens.

In the Rename text box type Orthocenter.

Click on the OK button at the bottom.

press Ctrl+ Z to undo the process.

Point to the triangle ABC.

Now press Ctrl+ Z to undo the changes.

Retain the triangle ABC with its angles.

Point to the angles. Let's now construct angle bisectors to the angles.
Select Angle Bisector tool >> click point B, A, C.


Click on points C,B, A >> click on points A, C, B.

For this, select the Angle Bisector tool from the tool bar.

Click on the points B, A, C.

C, B, A and A, C, B.

Hover the mouse on point of intersection

Click on Intersect tool >> click point of intersection.

Observe that the angle bisectors intersect at a point.

Let's mark this point as D using Intersect tool.

Point to segment BC.

Click Perpendicular Line tool >> click on point D >> click on segment BC.

Let's construct a line perpendicular to segment BC, passing through D.


Select the Perpendicular Line tool, click on point D and then on segment BC.

Point to the point of intersection.

Click on Intersect tool >> click point of intersection.

Observe that the perpendicular line intersects BC at a point.

Let's mark this point as E using Intersect tool.

Click on Circle with Centre through point tool >> click on point D >> click on point E.


Point to the incircle.

Let's now construct a circle with centre as D and which passes through E.

Click on Circle with Centre through point tool, click on point D and then point E.


A circle which touches all sides of the triangle is drawn.

This circle is the incircle to the triangle ABC.

Let us summarize what we have learnt.
Slide Number 6

Summary

In this tutorial we have learnt to,
  • Draw a triangle and measure its angles.
  • Display perimeter and area of the triangle
  • Show that sum of the angles of a triangle is 180 degrees
  • Show that, exterior angle is equal to sum of the interior opposite angles.
Slide Number 7

Summary

We have also learnt to draw,
  • Altitudes of the triangle and located the orthocenter.
  • An incircle to a triangle.
Slide Number 8

Assignment 1

As an assignment,


  • Draw a circumscribed circle to the triangle.
  • Hint: Draw perpendicular bisectors to the sides of the triangle.
Show the Assignment. Your assignment should look like this.
Slide Number 9

Assignment 2

Another assignment-


  • Draw medians to the triangle.
  • Mark the intersection point of medians.
  • Rename the point as centroid.
  • Hint: Mark midpoints of the sides.
  • Join the midpoint of each side with the opposite vertex.
Show the Assignment. Your assignment should look like this.
Slide Number 10

About Spoken Tutorial project

The video at the following link summarizes the Spoken Tutorial project.

Please download and watch it.

Slide Number 11

Spoken Tutorial workshops

The Spoken Tutorial Project team conducts workshops and gives certificates.

For more details, please write to us.

Slide Number 12

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.
Slide Number 13

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.

Contributors and Content Editors

Madhurig, Nancyvarkey, PoojaMoolya

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