Welcome to this Spoken tutorial on Basics of Triangles in GeoGebra.
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
Also we will learn to draw,
Altitudes of the triangle and locate the orthocenter An incircle to a triangle.
To record this tutorial, I am using; Ubuntu Linux OS version 14.04
GeoGebra version 5.0438.0-d
To follow this tutorial, learner should be familiar with Geogebra interface.
If not for relevant GeoGebra tutorials please visit our webiste.
I have opened a new GeoGebra window.
Before I begin, I will increase the font size to show the icons clearly.
Go to Options menu and select Font Size.
From the sub-menu select 18 pt radio button.
For this tutorial I will uncheck the Axes. Right-click on the Graphics view.
And from the Graphics menu, uncheck the Axes.
Now we will draw a triangle ABC.
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.
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.
Now let us learn to measure the angles of the triangle.
Click on the Angle tool. Click on the vertices B A C,
C B A
A C B
Values of the angles alpha, beta and gamma are displayed in the Algebra view.
Now we will move the overlapping labels.
Click on the Move tool and drag the labels to see them clearly.
Let us display the perimeter and area of the triangle.
Click on the Angle tool drop-down and select Distance or Length tool.
Click on the triangle ABC.
Perimeter of triangle is displayed on the triangle.
Now select the Area tool and click on the triangle ABC to display it.
Next we will find the sum of the angles of the triangle ABC using input bar.
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.
Observe the value of angle delta in the Algebra view. It is equal to 180 degree.
Now click on the Slider drop-down and select Text tool. Then click on the Graphics view.
A text window opens on the Graphics view.
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.
Now we will show that, the sum of the angles of the triangle is 180 degrees.
In the Edit text box type, Sum of the Angles is equal to
Select alpha from Objects drop-down + select beta from Objects drop-down + select gamma from Objects drop-down equal to select delta from Objects drop-down.
Observe the entered text and the values of the selected angles in the Preview box.
Click on the OK button at the bottom.
The text will be displayed on the Graphics view.
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.
Now we will draw a line extending segment BC.
Click on the Line tool, then click on points B and C.
Using Point tool we will mark a point D on line f next to C.
Now we will measure the exterior angle of the triangle ABC.
Click on the Angle tool and then click on the points DCA.
Using the Move tool, drag the overlapping labels of the angles and points.
Now, We will learn to change the colour of angle epsilon.
Right-click on angle epsilon. From the sub-menu, select Object Properties.
Preferences window opens.
In the Color tab change the colour to Maroon and drag the Opacity slider.
Close the Preferences window.
Now we will check if exterior angle is equal to sum of interior opposite angles.
In the input bar, open the parentheses. Inside the parentheses, select alpha from the symbols table.
Then press plus sign on the keyboard and select beta. Press Enter.
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.
Using the Move tool drag point C and observe the changes. We see that angle epsilon is equal to angle tau.
Next I will open a new window with triangle ABC and angles already drawn.
We will draw altitudes and an orthocentre to the triangle ABC.
For this first we will draw external lines on all the sides of triangle ABC.
Click the Line tool, then click on points A, B.
Similarly click on points B, C and A, C.
Now we will draw altitudes to the triangle ABC.
Click on the Perpendicular Line tool. Click on point A and line g.
Similarly click on point B and line h. Click on point C and line f.
The three altitudes of the triangle meet at a point.
Click on the Intersect tool and mark the point of intersection as D.
Point D is the orthocenter of the triangle ABC.
Let us rename point D as orthocenter. Right-click on point D.
From the sub-menu select Rename.
Rename text box opens.
In the Rename text box type Orthocenter. Click on the OK button at the bottom.
Now press Ctrl+ Z to undo the changes.
Retain the triangle ABC with angles.
Now let's construct angle bisectors to the angles.
For this, select the Angle Bisector tool from the tool bar.
Click on the points B, A, C.
C, B, A
A, C, B.
Observe that the angle bisectors intersect at a point.
Let's mark the point as D using Intersect tool.
Let us construct a line perpendicular to segment BC, passing through D.
Select the Perpendicular Line tool, click on point D and then on segment BC.
Observe that the perpendicular line intersects BC at a point.
Let's mark this point as E using Intersect tool.
Now, Let's construct a circle with centre D and which passes through E.
Click on Circle with Centre through point tool, click on point D and then click on 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.
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.
We have also learnt to draw, Altitudes of the triangle and located the orthocenter.
An incircle to a triangle.
As an assignment, Draw a circumscribed circle to the triangle.
Hint: Draw perpendicular bisectors to the sides of the triangle.
Your assignment should look like this.
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.
Your assignment should look like this.
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This is Madhuri Ganapathi from, IIT Bombay signing off. Thank you for watching.