GeoGebra5.04/C2/BasicsofTriangles/English
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

Slide Number 3
Learning Objectives 
Also we will learn to draw,

Slide Number 4
System Requirement 
To record this tutorial, I am using;

Slide Number 5
Prerequisites

To follow this tutorial, learner should be familiar
with Geogebra interface.

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 submenu select 18 pt radio button. 
Go to Options menu and select Font Size.

Rightclick on the Graphics view.
From Graphics menu, uncheck Axes. 
For this tutorial I will uncheck the Axes.
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.

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

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.

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 dropdown >> select Distance or Length tool.  Click on the Angle tool dropdown 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 dropdown >> 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.
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.

Now click on the Slider dropdown and select the Text tool.

Point to Edit box.
Point to Preview box. Point to Latex formula checkbox point Symbols and Objects dropdowns. 
The Text tool has,

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 dropdown + select beta from Objects dropdown + select gamma from Objects dropdown = select delta from Objects dropdown.  Select alpha from Objects dropdown + select beta from Objects dropdown + select gamma from Objects dropdown = select delta from Objects dropdown. 
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.

Point to segment BC.

Now we will draw a line extending segment BC.

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.

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

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. 
Rightclick on angle epsilon.
From the submenu select Object Properties. 
Rightclick on angle epsilon.
From the submenu, 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.

Point to Algebra view.
Point to epsilon and delta.

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

Drag point C.

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.

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.

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

Rightclick on point D.
From the submenu select Rename. 
Let us rename point D as orthocenter.
From the submenu 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.

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.

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.

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.
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,

Slide Number 7
Summary 
We have also learnt to draw,

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Assignment 1 
As an assignment,

Show the Assignment.  Your assignment should look like this. 
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Assignment 2 
Another assignment

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 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. 