GEOGEBRA TUTORIAL: GEOGEBRA BASICS

This tutorial firms up many of the concepts introduced in GeoGebra Worksheet: Triangles,
and also introduces some new features of GeoGebra.

This tutorial will be most helpful if you're trying everything in GeoGebra while you're reading.
Here's one way to do this:

Note: Things tend to change a bit over time.
Some of the information in this lesson may look slightly different on your own version of GeoGebra.
However, everything should be similar enough for you to recognize what to do.

CHECKED and UNCHECKED VIEW SUBMENU ITEMS

In the   View   submenu, a checked item means that it is visible.
These work as a toggle; when you click on a checked item, it becomes unchecked.
When you click on an unchecked item, it becomes checked.
Here are some examples:

axes visible; no grid axes visible; no grid grid visible; no axes grid visible; no axes axes visible; grid visible axes visible; grid visible no axes; no grid no axes; no grid
Axes visible; no Grid Grid visible; no Axes Axes visible; Grid visible no Axes; no Grid
GETTING A DROP-DOWN MENU FROM THE TOOLBAR

To get a drop-down menu from the toolbar, you must click the small arrow in the bottom right corner of a tool.
If you click anywhere else, you'll just make the tool active instead of getting the submenu.

getting a submenu

RENAMING AN OBJECT

To rename an object, right-click on the object and select ‘Rename’.
GeoGebra won't allow two different objects to have the same name:
it automatically renames, if needed, to prevent this from happening.

FREE versus DEPENDENT OBJECTS

Free objects are ones that can be freely moved with the MOVE tool.
Dependent objects depend on something else.

Here's a simple example to illustrate the difference.
To set things up:

You should now see what appears below:   points [beautiful math coming... please be patient] $\,A\,$ and $\,B\,$ are free; MIDPOINT was constructed as the midpoint of $\,A\,$ and $\,B\,$.

free and dependent objects

With the MOVE tool, you can move [beautiful math coming... please be patient] $\,A\,$ and $\,B\,$ wherever you please. (Try it!)
If you try to move MIDPOINT, it won't budge. The only way to control MIDPOINT is through its ‘parents’ $\,A\,$ and $\,B\,$.
(By the way, MIDPOINT is often called a ‘child’ of $\,A\,$ and $\,B\,$.)

If you hover over a dependent object, then you can see its dependency:

a dependent object

TRACING AN OBJECT

If you right-click on an object and check ‘Trace On’, then you can see a ‘trace’ of its movement in the geometry window.
Below, both [beautiful math coming... please be patient] $\,A\,$ and MIDPOINT are being traced.
(Point $\,A\,$ was moved with the MOVE tool; MIDPOINT followed accordingly.)
To make a trace disappear, uncheck ‘Trace on’.

trace on traced path

SHOWING AND HIDING OBJECTS and LABELS

Right-click on an object and uncheck ‘Show Object’ to make it disappear; its label also disappears.
Such an object is called a hidden object.
Notice that the bullet next to a hidden object is hollow; the bullet next to a visible object is filled-in (solid).

make an object disappear

If desired, you can uncheck ‘Show Label’ to make only a label disappear:

make a label disappear


UNDO/REDO

GeoGebra has a wonderful ‘undo’ feature.
If you ever goof anything up, just select   Edit-Undo   from the menu.
(There might also be an undo/redo shortcut at the right of the toolbar.)
You can undo multiple items.
You can redo anything that you undo.

undo and redo

GETTING A NEW GEOGEBRA WINDOW

The easiest way to get a new GeoGebra window is to select   File-New .
You are given the option of saving the current file.

LOWERCASE GREEK LETTERS FOR ANGLES

GeoGebra uses lowercase Greek letters to label angles.
For now, you should know the first three lowercase Greek letters:   alpha ($\,\alpha\,$), beta ($\,\beta\,$), and gamma ($\,\gamma\,$).

ADJUSTING LABEL POSITIONS

Sometimes, labels get positioned in an ugly way.
You can use the MOVE tool to adjust the position of the labels.

ugly labelingbetter labeling

DISPLAYING TEXT IN THE GEOMETRY WINDOW

You can display text in the Geometry Window using the ‘Insert Text’ tool, which is in the drop-down menu of the SLIDER tool.

‘Insert Text’ tool:   insert text tool

After you select a tool, instructions on its proper use appear to the right of the toolbar:

insert text instructions

Always look in this space to see how to use a tool!
For the ‘Insert Text’ tool, click anywhere in the drawing pad, and a text box appears:

text box

STATIC versus DYNAMIC TEXT

Static text is text that just sits there—it is static—it doesn't change.
Just type static text in the text box and click the button to accept.
Use the MOVE tool to put the text where you want it.

static text

Dynamic text is text that changes.
It's much more exciting and useful!

Quotation marks (",") are very important when you're creating dynamic text.
Characters inside quotation marks are displayed exactly as they appear.
Outside the quotation marks, a ‘+’ sign is used to put things together.
When you type a GeoGebra object outside the quotation marks, its current value will be displayed.

PRACTICE WITH DYNAMIC TEXT

Try to duplicate each of the examples below:

In this first example, create a single point, [beautiful math coming... please be patient] $\,A\,$.
In the ‘Insert Text’ box, type:   "A =" + A

dynamic text example
Type     "A =" + A     in the text box ...
dynamic text example

As you move $\,A\,$ around, the coordinates will change.

In this second example, create a line segment from [beautiful math coming... please be patient] $\,A\,$ to $\,B\,$.
Follow the directions illustrated below:

dynamic text example
Type this in the text box ...
dynamic text example

Move either endpoint and watch the length change!

In this third example, use the CIRCLE tool to create a circle with center [beautiful math coming... please be patient] $\,A\,$ and equation $\,c\,$.
Then, follow the directions illustrated below:

dynamic text example
Type this in the text box ...
dynamic text example

Move $\,A\,$ or $\,B\,$ and watch the dynamic text change!

CHANGING THE PROPERTIES OF DISPLAYED TEXT

You can change the properties of displayed text by right-clicking on the text box and selecting ‘Properties ...’ .

text properties
Changing the font, size, and color are all routine.
You see the changes immediately in the Geometry Window.

Two of the tabs, however, deserve some discussion:   ‘Position’ and ‘Advanced’.

MAKING TEXT FOLLOW A SPECIFIC OBJECT: the ‘POSITION’ TAB

You can set up text to follow (say) a point around the screen.
Get the ‘Properties ...’ box for the desired text.
Click on the ‘Position’ tab.
Type the name of the point you want the text to follow in the ‘Starting Point’ box:

setting up text to follow a point
Set up your text to follow point [beautiful math coming... please be patient] $\,A\,$ ...
text following a point

... and as you move $\,A\,$, the text follows!

DISPLAYING THE COORDINATES OF A POINT

GeoGebra uses   x(A)   and   y(A)   to denote the $\,x$-value and $\,y$-value of a point $\,A\,$.

SHOWING AN OBJECT UNDER SPECIFIED CONDITIONS

Suppose you only want to show an object (like text) when a certain condition is met.
You can use the ‘Advanced’ tab of the ‘Properties...’ box to do this!

For example, suppose you only want to show text when the [beautiful math coming... please be patient] $\,x$-value of a point is greater than zero.
Get the ‘Properties ...’ box for the desired text.
Click on the ‘Advanced’ tab.
Follow the instructions below:

showing the name and value meeting a specified condition failing to meet a specified condition
Set up the desired condition. Here, the [beautiful math coming... please be patient] $\,x$-value is $\,1.2\,$,
which is greater than zero.
Thus, the text is showing.
Here, the $\,x$-value is $\,-0.18\,$,
which is not greater than zero.
Thus, the text is not showing.

EVERY GEOGEBRA OBJECT HAS ITS OWN PROPERTIES BOX

Indeed, every GeoGebra object has its own ‘Properties ...’ box.
This ‘Properties ...’ box gives you some special labeling features:
you can show only the NAME of an object; both the NAME and VALUE; or only the VALUE.

showing the name and value
set up point [beautiful math coming... please be patient] $\,A\,$ to show both name and value ...
showing the name and value

... and here's what you'll see

Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Introduction to Polygons


On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
(MAX is 24; there are 24 different problem types.)