GeoGebra Quickstart
A quick reference guide for GeoGebra
GeoGebra is free educational mathematics software that joins dynamic geometry, algebra and calculus.
hurryingIn the most simple manner, you can do constructions including points, vectors, g-ments, lines, and conic ctions as well as functions, which can be altered dynami-cally by mou afterwards. On the other hand, also the direct input in school-notation like
g: 3x + 4y = 7 or c: (x – 2)2 + (y – 3)2 = 25 is possible, and a range of commands in-cluding differentiation and integration are at your disposal. The most remarkable fea-ture of GeoGebra is the dual view of objects: every expression in the algebra window corresponds to an object in the geometry window and vice versa.
In the following, you will get acquainted to GeoGebra by examining three examples. You should work them out one after the other and not forget to try out the given tips, too.
Example 1: Circumcircle of a triangle
Example 2: Tangents to a circle
Example 3: Derivative and tangent of a function
After starting GeoGebra, the window depicted below appears. By means of the con-struction tools (modes) in the toolbar you can do constructions on the drawing pad by mou. At the same time the corresponding coordinates and equations are displayed in the algebra window. The input text field is ud to enter coordinates, equations, commands and functions directly; the are displayed at the drawing pad immedi-ately after pressing the enter key. Geometry and algebra side by side:
Algebra
Window
Toolbar Input Field
Undo/Redo Drawing Pad Input Options
Example 1: Circumcircle of a triangle
Task: Plot a triangle A, B, C and construct its circumcircle using GeoGebra.世界上最大的客机
Construction using the mou
Choo the mode “Polygon” from the toolbar (click on the small arrow at the third icon from the left). Now click on the drawing pad three times to create the vertices A, B, and C. Clo the triangle by clicking on A again.
Next, choo the mode “Line bictor” and construct two line bictors by
clicking on two sides of the triangle.
In the mode “Interct two objects” you can click on the interction of both
line bictors to get the center of your triangle’s circumcircle. To name it “M”, click on it with the right mou button (Mac OS: ctrl-click) and choo “Re-
name” from the appearing menu.
To finish the construction, you have to choo the mode “Circle with center
through point” and to click first at the center, then at any vertex of the triangle.
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Now choo the mode “Move” and u the mou to change the position of
any of the vertices – you will experience the meaning of “dynamic geometry”. Some tips
Try the “Undo” button on the right side of the toolbar.
To hide an object, right click on it (Mac OS: ctrl-click) and uncheck “Show object”.
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The appearance of objects (color, type of line, ...) can be changed easily: just u the right mou button (Mac OS: ctrl-click) again to click on the object and choo “Properties” from the appearing context menu.
In the menu “View” algebra window, axes, and grid can be hidden or shown.
In order to change the position of the drawing pad, choo the mode “Move draw-ing pad” and simply u the mou to drag it.
The menu “View – Construction Protocol“ provides a table listing all the steps you
took while doing your construction. This allows you to redo the construction step by step by the u of the arrow keys, and also to modify the order of various steps afterwards (e menu “Help” of the construction protocol). Moreover, you are able to u the menu “View” to hide or show unwanted columns.
Further information on constructions by mou can be found in menu “Help“, c-tion “Geometric input”.
Construction using the input text field
We are now going to do the same construction as above using the input text field, so you will need a new drawing pad (menu “File – New”). Then, type the following com-mands into the input text field at the bottom of the screen and press the enter key after every line.
A = (2, 1)
B = (12, 5)
C = (8, 11)
Polygon[A, B, C]
l_a = LineBictor[a]
l_b = LineBictor[b]
M = Interct[l_a, l_b]
Circle[M, A]
Some tips
Automatic completion of commands: after entering the first two letters of a com-mand, it will be displayed automatically. If you want to adopt the suggestion, press the enter key, otherwi just continue typing.
It is not necessary to key in every command, you can also choo it from the list
of commands that is found at the right next to the input text field.
Clicking at the icon “Input“ (bottom left) activates the mode “Input field”. In this mode you can click on an object from the algebra window or drawing pad to copy its name into the input text field.
For more tips concerning the input text field click on the question mark in the bot-tom left corner.
You will obtain especially good results from your work with GeoGebra by combining the advantages of both input forms, mou and input text field.
Example 2: Tangents to a circle
Task : Using GeoGebra, construct the circle c: (x - 3)² + (y - 2)² = 25 and its tangents through the point A = (11, 4).
Construction using input text field and mou
Inrt the equation of the circle c: (x - 3)² + (y - 2)² = 25 into the input text field and press the enter key (tip : the exponent can be found in the list to the right of the input field.)
Enter the command C = Center[c] into the input text field.
Construct the point A by keying in A = (11, 4).
Now choo the mode “Tangents“ and click on the point A and the circle c.
After choosing the mode “Move“, drag the point A with the mou and ob-rve the movement of the tangents.
You should also try to drag the circle c and have a look at its equation in the algebra window.
Some tips U the tools in the rightmost toolbar menu to zoom in or out. If you have a mou wheel,
try ctrl + mou wheel to zoom. It is possible to alter the equation of the circle directly in the algebra window by double-clicking on it.
Further information on the possibilities of the input text field can be found in the menu “Help“, ction “Algebraic input“.
Example 3: Derivative and tangent of a function
Task: U GeoGebra to construct the function f(x) = sin(x), its derivative and its tan-gent to a point on f plus slope triangle.
Version 1: Point on function
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function
f(x) = sin(x) into the input text field and press the enter key.
Choo the mode “New Point” and click on the function f. This creates a point
A on f.
Next choo the mode “Tangents“ and click on the point A and the function f.
Change the tangent’s name to t (right mou button (Mac OS: ctrl-click), “Re-name”).
Type the command s = Slope[t].
After choosing the “Move” mode, drag the point A with the mou and obrve the movement of the tangent.
Type
B = (x(A), s) and switch on the trace of this point (click on B with the right
mou button (Mac OS: ctrl-click)). x(A) gives you the x-coordinate of point A.
Choo the mode “Move” and drag A with the mou – B will leave a trace.
一句美好的祝福语Type the command Derivative[f].
Some tips
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Inrt a different function, e. g. f(x) = x³ - 2x² into the input text field; immediately, its derivate and tangent will be displayed.
Choo the “Move” mode and drag the function’s graph with the mou. Ob-rve the changing equations of the function and its derivative.
