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Table of Contents

About this Guidebook... vi
CHAPTER 1: LEARNING THE BASICS
First Steps.... 12 Constructing Objects.. 110
CHAPTER 2: USING THE MENUS... 21
File Menu.... 22 Edit Menu.... 25 Options Menu... 27 Help Menu.... 212
CHAPTER 3: USING THE POINTER TOOLBOX. 31
Pointer... Rotate... Dilate... Rotate and Dilate... 34 35
CHAPTER 4: USING THE POINTS TOOLBOX.. 41
Point.... Point on Object.. Intersection Point(s).. 44
CHAPTER 5: USING THE LINES TOOLBOX.. 51
Line.... Segment... Ray... Vector... Triangle... Polygon... Regular Polygon... 59
CHAPTER 6: USING THE CURVES TOOLBOX.. 61
Circle... Arc... Conic... 64
CHAPTER 7: USING THE CONSTRUCT TOOLBOX
Perpendicular Line... 72 Parallel Line... 73 Midpoint... 74 Perpendicular Bisector... 75 Angle Bisector... 76 Vector Sum... 77 Compass... 78 Measurement Transfer... 79 Locus... 711 Redefine Point... 713 Redefine Object.. 714
CHAPTER 8: USING THE TRANSFORM TOOLBOX. 81
Reflection.... Symmetry.... Translation... Rotation... Dilation... Inverse... 86 87
CHAPTER 9: USING THE MACRO TOOLBOX
How to create a macro... Initial Object... Final Object... Define Macro...
CHAPTER 10: USING THE CHECK PROPERTY TOOLBOX.. 101
Collinear... Parallel... Perpendicular... Equidistant... Member... 106
Table of Contents (continued)
CHAPTER 11: USING THE MEASURE TOOLBOX.. 111
Distance & Length... Area.... Slope... Angle... Equation & Coordinates... Calculate... Tabulate... 1111
CHAPTER 12: USING THE DISPLAY TOOLBOX.. 121
Label... Comments.... Numerical Edit... Mark Angle... Fix/Free... Trace On/Off... Animation.... Multiple Animation... 1210 1211
CHAPTER 13: USING THE DRAW TOOLBOX.. 131
Hide/Show... Color... Fill... Thick... Dotted... Modify Appearance... Show/Hide Axes... New Axes.... Define Grid.... 1310

INDEX.... INDEX1

About this Guidebook
The Cabri Geometry II Guidebook contains user information about the Cabri Geometry II software. It provides descriptions, procedures, illustrations, and examples for using the software features on Macintosh computers, and Windows and MS-DOS-based PCs. 4 Many of the procedures, illustrations, and examples are virtually the same for the different computer types. Significant differences between the Macintosh, Windows, and DOS versions are identified for your convenience. Most of the illustrations are from the Macintosh version; several are from the Windows and DOS versions. Due to space limitations, we could not show every illustration for each version. Therefore, some illustrations in this guidebook may be slightly different on your computer. Key names are shown in small capital letters such as CTRL for the Control key and ESC for the Escape key. The RETURN key on the Macintosh and the ENTER key on the PC keyboard perform the same function. In this guidebook, Press ENTER means to press either ENTER or RETURN.

Structure

The Cabri Geometry II Guidebook contains the following chapters and appendices: 4 Chapter 1 describes the basic operations for using Cabri II, starting with checking system requirements for installing the software, through constructing objects, to saving and printing a construction file. Chapter 2 describes the Cabri II menus and provides step-by-step procedures for using them. Chapters 3 through 13 describe the Cabri II tools and provide step-by-step procedures for using them. Each chapter discusses a specific group of Cabri II tools.

Definitions

The following definitions will help you in your understanding of this guidebook. point click double-click drag When used as an instruction, point means to place the screen pointer on top of the object you wish to select. Click means to press and release the mouse button quickly, usually when pointing to a specific location Double-click means to click the mouse button twice in succession. Drag means to point to the object you want to drag, press and hold the mouse button to select the object, and move the screen pointer to a new location. Release the mouse button to stop dragging. When used as an instruction, modify means to change the appearance, size, location, or orientation of the object. Marquee outline is the outline of an object in animated dots, similar to a movie marquee. Marquee rectangle is the selection rectangle that appears when you drag with the Pointer tool from an unoccupied location in the drawing window. When you release the mouse button, objects that lie completely within the rectangle are selected.
modify marquee outline marquee rectangle
Chapter 1: Learning the Basics
This chapter provides descriptions and examples of basic operations in Cabri Geometry II. Becoming familiar with these items will enhance your usage. Differences between the Macintosh, Windows, and MS-DOS versions are explicitly described where applicable. For convenience, DOS will be used in the remainder of this guidebook to mean MS-DOS. The following topics are discussed: FIRST STEPS
Checking system requirements Installing Cabri Geometry II Starting Cabri Geometry II Optimizing your Macintosh system configuration Changing your Macintosh system configuration using Cabri Geometry II Using Cabri Geometry II on a network The Cabri Geometry II window Accessing on-line help About menus and toolboxes

CONSTRUCTING OBJECTS

Pointers that guide you Creating and selecting points Handling ambiguities Determining dependent and independent objects Dragging Using the Undo/Redo command Deleting objects Changing the appearance of objects Labeling objects Scrolling the drawing window Saving and printing

First Steps

Checking system requirements

Options Menu

The Options menu contains commands that relate to showing attributes of each construction tool, setting defaults, and defining the contents and configuration of the toolbar.

Hide/Show Attributes

The Hide/Show Attributes command hides and shows the attributes toolbar. You can toggle the command from one to the other.
Defaults. (Macintosh only)
The Defaults. command for the Macintosh version provides options that allow you to select default colors and attribute settings for various classes of objects. The defaults can be saved to the Cabri Geometry II preference file. If the Cabri Geometry II preference file is placed in the Cabri Geometry II preferences folder or the system preferences folder, the settings saved in this file will be activated each time you open Cabri Geometry II. The Default Options dialog box is shown below. Click the Factory Settings button to return each default to its factory specification.

Preferences.

The Preferences. command lets you specify particular aspects of the program related to loci, the coordinate system, measurements, and equation formats. A dialog box, as shown on the next page, appears when you select this command. The options are described below the illustration. The settings specified in Preferences for the Macintosh and Windows versions can be saved to a Cabri Geometry II preferences file. This file also contains the defaults specified using the Defaults command. This file must reside in the Cabri Geometry II preferences folder or your Macintosh system preferences folder for it to be automatically referenced at run time. If more than one Cabri Geometry II preferences file is in either of these folders, Cabri Geometry II will use the first file that it finds. The Cabri Geometry II preferences file and preferences folder are created when a preference file or tool configuration file is saved to disk for the first time. This menu option in the DOS version is very similar to the Macintosh version. However, only one preference file (cabri2.prf) can exist in the same subdirectory. Additionally, when you select Preferences and save to a file, the new preferences will be used when you start Cabri Geometry II the next time. To change preferences, go back to Preferences and change the settings or set them back to Factory Settings.

Options Menu (Continued)

Macintosh, DOS Windows

(DOS only)

Loci options
This option applies to all loci constructed in the drawing. The Locus tool performs a linear interpolation of the loci calculated. Therefore, the more objects in the locus, the smoother it will appear. You can change this number in this dialog box for the default setting or for a specific locus by selecting the locus, and then changing the values in this dialog. You can also change the number of objects in the locus by selecting the locus, and then pressing + or on the keyboard to increase or decrease the number of objects. Selecting the Link points option connects adjacent points with a solid line. Selecting the Envelope option draws only the envelope of a line as the locus rather than the locus of the line.

Languages (Macintosh, Windows)
The Languages command lets you change the language of Cabri Geometry II menus, dialog boxes, messages, and labels. You may change the language at any time during a session. Macintosh Windows
The Language settings command opens a dialog box that lets you: Choose the language to be used the next time you start Cabri Geometry II. (Macintosh only) Choose to attach a language to the Cabri Geometry II software. Cabri Geometry II can recognize any language module that is in the same folder. This command integrates the language as part of the Cabri Geometry II software. (Macintosh only) Choose to exclude a language from the Cabri Geometry II software. If the And save in a file option is selected, the language will be saved in a separate file and can be reattached later. If the And save in a file option is not selected, the language will not be available unless you reinstall the software (for core languages) or place a language file in your Cabri folder.
Font (Macintosh, Windows)
The Font command in the Macintosh and Windows versions lets you view the fonts installed on your computer. The symbol in the Macintosh version is shown next to the default font. The default font applies to labels, comments, numerical values, and properties. You can specify fonts independently for the Label, Comments, or Numerical Edit tools by first selecting the tool, and then changing the font in this menu. Point to another font to select it as the new default font. Note: The Windows version dialog box lets you set the font size and style.

Size (Macintosh)

The Size command in the Macintosh version lets you view the font sizes available on your computer. The point sizes in outlined text are sizes that your Macintosh should display without distortion. The symbol is shown next to the default size. The default size applies to labels, comments, numerical values, and properties. You can specify size independently for the Label, Comments, or Numerical Edit tools by first selecting the tool, and then changing the size in this menu. Point to another size to select it as the new size. For classroom demonstrations, it is useful to set the default font size at 14 or 18 points.

Style (Macintosh)

The Style command in the Macintosh version lets you view the text styles available on your computer. Text styles are independently applied to text and may be combined. For example, you can specify bold-italic text by selecting each style type separately. The default style applies to labels, comments, numerical values, and properties. You can specify style independently for the Label, Comments, or Numerical Edit tools by first selecting the tool, and then changing the style in this menu.
Help Menu (Windows and DOS), A (Macintosh)
The Help menu in the Windows and DOS versions, and A in the Macintosh version, let you view helpful information about each toolbar icon and information about the Cabri Geometry II software.
Keyboard shortcut: F1 (DOS)
The Help command displays a description of the selected toolbar icon in the Help window at the bottom of the Cabri Geometry II screen. For the Macintosh version, click on A to open the Help window.

About (Cabri II)

The About (Cabri II) command displays information about Cabri Geometry II that includes authors names, copyright notice, and the version number of the software.
Chapter 3: Using the Pointer Toolbox
The Pointer toolbox contains the tools associated with Cabri Geometry II pointer features. These features allow you to select objects and to perform freehand transformations. The illustration below shows the location of the Pointer toolbox on the Cabri Geometry II toolbar, along with its pull-down menu. Procedures for using Pointer tools, including examples, are presented in this chapter in the order in which the tools appear on the pull-down menu.

Pointer toolbox

Pointer Rotate Dilate Rotate and Dilate

Pointer

The Pointer tool selects or moves objects in a freehand manner. Press and hold the mouse button in unoccupied space to observe all basic and independent points which display as flashing. You can also double-click on a label, comment, numerical value, or the table to automatically invoke the appropriate edit tool for the object.
Selecting or moving objects
1. 2. Select Pointer from the Pointer toolbox. Selecting: Select an object by pointing and clicking when the cursor message appears for that object. Select multiple objects by pressing the SHIFT key when selecting objects, or by enclosing them in a marquee rectangle as shown in the example below. Deselect an object by pointing to an unoccupied location and clicking.

Select a dilation point.

Rotate and Dilate
The Rotate and Dilate tool rotates and dilates an object about its geometric center or a defined point in a freehand manner. See the Rotate tool and the Dilate tool for more information.

Using Rotate and Dilate

Select Rotate and Dilate from the Pointer toolbox.
Note: You can rotate and dilate an object automatically by using the Animation tool when the Rotate and Dilate tool is visible on the toolbar. See the chapter Using the Display Toolbox for more information about Animation. Examples Freehand rotation and dilation of an object about its geometric center:
Drag object in a circular or linear path.
Freehand rotation and dilation of an object about a defined point:
Select a transformation point. Drag object in a circular or linear path.
Chapter 4: Using the Points Toolbox
The Points toolbox contains the tools associated with creating or constructing points in Cabri Geometry II. These features allow you to create points anywhere in the plane, on objects, or at the intersection of two objects. The illustration below shows the location of the Points toolbox on the Cabri Geometry II toolbar, along with its pull-down menu. Procedures for using tools in the Points toolbox, including examples, are presented in this chapter in the order in which the tools appear on the pull-down menu.

Points toolbox

Point Point on Object Intersection Point(s)
The Point tool creates points that can be placed anywhere in the plane, on existing objects, or at the intersection of any two objects. If you create a point on an object, it remains on that object throughout any changes made to the point or to the object. If a point is at the intersection of two objects, the point remains at the intersection throughout any changes made to the object(s). If you change the objects so that they no longer intersect, the intersection point disappears, but reappears if the objects intersect again.

Creating a point

1. 2. Select Point from the Points toolbox. Move the cursor to any location in the plane where you want a point. When the cursor message appears, click once to create a point. If in free space, a cursor message does not appear. Note: You do not have to select the Point on Object or Intersection Point(s) tools to create a point on an object or at an intersection.

Modifying a segment

Change a segment by dragging either endpoint. Translate a segment by grabbing away from the endpoints, and dragging it.
The Ray tool creates a ray defined by an initial endpoint and extending infinitely in a specified direction. Note: You can constrain the slope to 15-degree increments by pressing the SHIFT key when creating or modifying a ray.

Creating a ray

1. Select Ray from the Lines toolbox.
Click to create or select the initial endpoint of the ray.
Position the ray in the desired orientation, and click to specify direction and slope. If the ray is created in free space, a point is not created. If the ray is not in free space, it is attached to a second point.
Click to specify the slope.

Modifying a ray

Translate a ray without changing its direction and slope by selecting the Pointer tool from the Pointer toolbox. Then using the Pointer: For a ray constructed with a single point, drag the point. For a ray constructed with two basic points, grab the ray away from the points and drag.
Change the direction and slope of a ray using the Pointer tool: 4 To change a ray constructed with a single point, grab the ray away from the point and drag. Press the SHIFT key to constrain the slope to 15-degree increments. To change a ray constructed with two basic points, drag either of the points. Changing a ray constructed with a dependent point is relative to the object to which it is attached. You may drag the object or the point, depending on the construction.

Vector

The Vector tool creates a vector defined by magnitude and direction with a tail (initial endpoint) and head (final endpoint).

Creating a vector

1. Select Vector from the Lines toolbox.
Click to create or select the tail of the vector.

Create the tail.

Move the pointer to the location for the head, and click to create or select the head of the vector.

Create the head.

Creating a regular polygon
1. Select Regular Polygon from the Lines toolbox.
Click to create or select the center point.

Create the center point.

Move the cursor from the center point, and click to specify the radius of a regular polygon. The number of sides is displayed at the center point.

Specify the size.

To create a regular convex polygon, move the cursor clockwise from its current position. To create a regular star polygon, move the cursor counterclockwise, and click when the regular polygon is the desired size. Note: If you move beyond 30 sides or 180 degrees from the initial vertex and the center point, a convex polygon becomes a star polygon. A fraction is displayed at the center point. The numerator determines the number of sides; the denominator, the number of times the star has crossed. The maximum star is 30/13; the minimum is 5/2.

Rotate clockwise.

Pentagon.
Regular Polygon (Continued)
Modifying a regular polygon
Move a regular polygon as an object by dragging one of its sides. Change a polygon by dragging any of its vertices. Dragging the center point changes the size of the regular polygon since the original vertex is anchored (location dependent). Example
1. Create the center point. 2. Specify the size.
3. Rotate counter-clockwise.

4. 7/3 star polygon.

Chapter 6: Using the Curves Toolbox
The Curves toolbox contains the tools associated with curve features in Cabri Geometry II. These features allow you to create curved objects, including ellipses, parabolas, and hyperbolas. The illustration below shows the location of the Curves toolbox on the Cabri Geometry II toolbar, along with its pull-down menu. Procedures for using tools in the Curves toolbox, including examples, are presented in this chapter in the order in which the tools appear on the pull-down menu.

Curves toolbox

Circle Arc Conic

Circle

The Circle tool creates a circle defined by a center point and a radius that can be specified in free space, at an existing point, or on an object. Note: You can constrain the radius to integer values by pressing the SHIFT key while defining or modifying the radius.

Symmetry

The Symmetry tool reflects the image of an object 180-degree with respect to a point.
Creating a symmetrical image
1. Select Symmetry from the Transform toolbox.
Select the object to reflect 180 degrees.
Select the object to reflect
Select the point of symmetry.
with respect to this object
The symmetric image is created.
Modifying a symmetrical image
Change a symmetrical image by changing the original object or by moving the point of symmetry. Because it is a dependent object, you cannot change a symmetrical image directly.

Translation

The Translation tool creates the image of an object translated by a specified, previously defined vector.

Translating an object

1. Select Translation from the Transform toolbox.
Select the object to translate.

Translate this polygon

Select the vector that defines the translation direction and distance.
Select the translation vector.

by this vector

The translated image is created.

Modifying a translation

Move a translated image by dragging the vector head or tail to a new location. The translated image changes according to the changes of the vector or changes to the original object. Because it is a dependent object, you cannot change the translated image directly.

Rotation

The Rotation tool rotates an object by a specified angular value with respect to a point. Note: The angular value may be any measurement or numerical value, regardless of units. The units are presumed to be degrees by the software. A positive angular value rotation is performed in a counter-clockwise direction. To create specific angles of rotation, please refer to Numerical Edit in the chapter Using the Display Toolbox.

Rotating an object

1. Select Rotation from the Transform toolbox.
Select the object to rotate.

Rotate this polygon

Select the point of rotation.
Select the rotation point.

around this point

Select the angular value of rotation.

using this angle

The rotated image is created.

Modifying a rotation

Change the rotated image by either modifying the figure that defines the angle of rotation, editing the value created by Numerical Edit, moving the rotation point, or changing the original object. Because it is a dependent object, you cannot change the rotated image directly.

Dilation

The Dilation tool dilates an object by a specified factor with respect to a specified point. Note: This factor may be any measurement or numerical value, regardless of units. The value is presumed to be unit-less. To create specific factors of dilation, please refer to Numerical Edit in the chapter Using the Display Toolbox.

Macro toolbox

Initial Object Final Object Define Macro

How to create a macro

A macro constructs final objects based on initial objects. Intermediate objects are not constructed. This feature allows easy construction of complex figures and is the primary method for constructing fractals. You can save macros on disk for later use. Macros are automatically saved with any file in which they are used. To create a macro: 1. 2. 3. Select the initial objects required to define the final object(s). Select the final object(s), and then, if necessary, change the attributes of the object(s) as they will appear in the final construction. Define the macro for inclusion in the Macro toolbox. The macro is then available for use.
Read the following rules, and then refer to the step-by-step procedures that follow them.
Rules for creating macros
4 Initial objects must allow the construction of all final objects. Final objects must be determined by the initial objects. A macro must respect the logical structure of the figure as it was constructed. An object cannot exist without the points that define it. For example, a triangle cannot exist without its vertices. Therefore, when you select an object as an initial object, the macro is able to refer to the points that define the object. When you select Define Macro, a macro generates its final objects with the objects existing attributes. You can change these attributes during an intermediate step before you select Define Macro. In this way, you can hide objects (using Hide/Show in the Display toolbox) that were selected as initial objects. Because macros are intended as general purpose construction tools, like those in the Construct toolbox, comments and labels cannot be defined as final objects. You can select measurements and numerical values as final objects, but any text attached will not be duplicated when the macro executes. The location of an arbitrary point on an object is determined by a random-number generation. Therefore, the position of the point will be uncertain if it is selected as a final object. If the initial objects are different types (for example, lines and circles are different types), they are not used in any order. If the initial objects are the same type, the macro uses them in the order in which they were selected as initial objects. The number of objects created by a macro is limited only by available system memory. Macros are automatically saved with any construction in which they are used. You can also save macros in a tool configuration file (see Options Menu in the chapter "Using the Menus"). The first final object you select is considered the primary object of the macro. If a name is entered in the Name for first final object field, it will be the cursor message when the cursor is in the vicinity of the primary object. For the Macintosh, the Name for first final object field is found under the More option in the Macro dialog box. For the Windows and DOS versions, the Name for first final object field is already visible in the dialog box. To save multiple definitions for a single macro, select the initial and final objects for the new definition, and save it with the same name. The dialog box generated in Define Macro allows you to select previous macros when saving a macro. For example, you may want to define a macro that constructs a triangle with vertices at the midpoints of an initial triangle, a polygon with vertices at the midpoints of a three-sided polygon, and a triangle with vertices at the midpoints of a three-sided regular polygon. A single macro can perform all of these operations if each case is identified with appropriate initial and final objects and saved to the same macro file.

Enter the name that you want to appear as a cursor message when the cursor is in the vicinity of the first object created by the macro.

Help for this macro

Enter the message that you want to appear in the help window when the macro is selected.

Define Macro (Continued)

Save to file This button is a toggle. Click on it to change the OK to OK and save, and vice versa. Click on OK to save the macro for use in your construction. The macro is not saved to a separate file but is saved with your construction. Once saved, the macro can be used in future Cabri Geometry II sessions. Click on OK and save to generate a save file dialog that allows you to save the macro to a file you specify. Macros saved to individual files can be recalled in future constructions by using Open in the File menu to open the macro file.

OK / OK and save

Specifying a macro
1. Select Define Macro from the Macro toolbox.
Enter the requested information into the dialog box to save your macro. If you receive a warning message instead of the dialog box, a problem exists in the definition of initial and final objects. Review Rules for creating macros at the beginning of this chapter, and redefine your initial and final objects.

Define Macro dialog box.

Select a new macro.
Select an appropriate object.
Click to apply the macro.
Chapter 10: Using the Check Property Toolbox
The Check Property toolbox contains the tools associated with Cabri Geometry II property features. These features allow you to check the validity of geometric properties in general. Results are reported in text, which can be edited with the Comments tool located in the Display toolbox. The illustration below shows the location of the Check Property toolbox on the Cabri Geometry II toolbar, along with its pull-down menu. Procedures for using Check Property tools, including examples, are presented in this chapter in the order in which the tools appear on the pull-down menu.

Check Property toolbox

Collinear Parallel Perpendicular Equidistant Member

Collinear

The Collinear tool evaluates three selected points to determine whether or not they lie on the same line. The results are reported in text.

Tabulate (Continued)

Using Tabulate
1. Select Tabulate from the Measure menu.
Define the table by dragging the marquee rectangle to size the table. You can resize the table by dragging the lower right corner.
Drag rectangle to size the table.
Point to a numerical value, and click to enter it into the table.
Click on each value to be tabulated.
Area 1.2601 cm2 Radius 0.63 cm This number
Press TAB to record new values. Note: At least one value must change before a new row is entered. To tabulate values automatically, first select the table, and then animate the construction using Animation or Multiple Animation (in the Display toolbox). When selected, the table displays with a marquee rectangle around it.
Press the TAB key to tabulate entries.

Adding values

1. Select Tabulate, and then point to the value and click. The new value is added in the next available column and row. Blank cells in the new column will be filled with a hyphen (-). 2. Press TAB to record new values.
Sizing a table and deleting columns and rows
Sizing a table: 1. Click on the table. An edit window is displayed around the table. 2. Point to any column divider in the first row. The cursor changes to the column width 3 cursor. 3. Drag the column to modify its width.
New column width. Point to the column divider and drag.
Deleting a column: 1. Click in the first row of a column (the title column) to select the column. The column is highlighted. 2. Press DELETE or select Clear in the Edit menu to delete the column.
Point and click in the first row of a column.
Deleting a row: 1. Click in a row of the first column (the sequentially numbered column) to select the row. The row is highlighted. 2. Press DELETE or select Clear in the Edit menu to delete the row.
Point and click in a row of the first column.
Chapter 12: Using the Display Toolbox
The Display toolbox contains the tools associated with display features in Cabri Geometry II. These features allow you to annotate your constructions or animate objects. The illustration below shows the location of the Display toolbox on the Cabri Geometry II toolbar, along with its pull-down menu. Procedures for using Display tools, including examples, are presented in this chapter in the order in which the tools appear on the pull-down menu.

Display toolbox

Label Comments Numerical Edit Mark Angle Fix/Free Trace On/Off Animation Multiple Animation

I-beam pointer, 1-10 Initial Object tool, 9-3 initial point of a line, 5-2 installing the software, 1-2 Intersection Point(s) tool, 4-4 Inverse tool, 8-7
Label tool, 12-2 labeling objects, 1-19, 12-2 language, changing, 2-10 Line tool, 5-2 Lines toolbox, 5-1 Locus tool, 7-11 low memory message, 1-4
Macro toolbox, 9-1 magnifying glass pointer, 1-10 Mark Angle tool, 12-7 Measure toolbox, 11-1 Measurement Transfer tool, 7-9 measuring objects, 11-2 Member tool, 10-6 memory, available for application, 1-4 Menu bar, description, 1-6 menus, options, 1-8 Midpoint tool, 7-4 Modify Appearance tool, 13-7 modifying a point on an object, 4-3 angle bisectors, 7-6 appearances, 13-9 arcs, 6-3 circles, 6-2 comments, 12-4 compass circles, 7-8 conics, 6-4 dilations, 8-6 equation or coordinates, 11-6
File menu, 2-2, 2-3, 2-4 Fill tool, 13-4 filling an object with color, 13-4 Final Object tool, 9-4 Fix/Free tool, 12-8 fixing or freeing points, 12-8 Font command, 2-11 freehand rotation of an object, 3-5 function buttons, calculate window, 11-8 functions and syntax, calculate window, 11-9

Index-2

modifying (continued) inverse points, 8-7 labels, 12-2 lines, 5-2 loci, 7-12 marked angles, 12-7 modifying (cont.) measurement transfers, 7-10 midpoints, 7-4 numerical values, 12-6 parallel lines, 7-3 perpendicular bisectors, 7-5 perpendicular lines, 7-2 points, 4-2 rays, 5-5 reflections, 8-2 regular polygons, 5-10 rotations, 8-5 segments, 5-4 symmetrical images, 8-3 traces, 12-9 translations, 8-4 triangles, 5-7 vector sum, 7-7 vectors, 5-6 moving measurements area, 11-3 of an object, 11-2 of angles, 11-5 slope, 11-4 moving objects, 3-2 Multiple Animation tool, 12-11
Page Setup command, 2-3, 2-4 paint brush pointer, 1-10 paint bucket pointer, 1-10 paper size and orientation, 2-3, 2-4 Parallel Line tool, 7-3 Parallel tool, 10-3 Paste command, 2-5 Perpendicular Bisector tool, 7-5 Perpendicular Line tool, 7-2 Perpendicular tool, 10-4 Point on Object tool, 4-3 Point tool, 4-2 Pointer tool, 3-2 Pointer toolbox, 3-1 pointers, display types, 1-10 pointing hand pointer, 1-10 Points toolbox, 4-1 Polygon tool, 5-8 Preferences command, 2-7 Print command, 2-4 Printer Setup command, 2-4 printing a construction file, 1-22, 2-4 printing options, 2-4 printing to scale, 2-3, 2-4

Quit command, 2-4

network operation, 1-3 New Axes tool, 13-9 New command, 2-2 Ray tool, 5-5 Redefine Object tool, 7-14 Redefine Point tool, 7-13 redefining an object, 7-14 redefining a point, 7-13 Redo command, 1-17, 2-5 Reflection tool, 8-2 Regular Polygon tool, 5-9 removing selected objects, 2-5 Replay Construction command, 2-6 replaying each step of a construction, 2-6 returning to a recently saved version, 2-3 Revert command, 2-3 Rotate and Dilate tool, 3-5 Rotate tool, 3-3 rotating an object, 3-3, 8-5 rotating an object automatically, 3-3 Rotation tool, 8-5

GEOMETRY II
Getting Started with Cabri Geometry II for Macintosh, Windows and MS-DOSa

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Getting Started with Cabri Geometry II for Macintosh, Windows, and MS-DOS

Dive into Geometry

About Cabri Geometry II
Cabri Geometry II lets you construct and explore geometric objects interactively. Jean-Marie Laborde and Franck Bellemain developed Cabri Geometry II at the Institut d'Informatique et Mathmatiques Appliques de Grenoble (IMAG), a research lab at the Universit Joseph Fourier in Grenoble, France, in cooperation with the Centre National de la Recherche Scientifique (CNRS) and Texas Instruments. Texas Instruments, the publisher for Cabri Geometry II in the United States and Canada, is pleased to bring computer-based geometry to classrooms. The geometric foundation of this easy-to-use software encourages exploring and conjecturingfrom simple shapes to advanced projective and hyperbolic geometry.

About the Developers

Jean-Marie Laborde is founder and Research Director of Laboratoire de Structures Discrtes et de Didactique (LSD2), a research laboratory within IMAG. He graduated in mathematics at cole Normale Suprieure in Paris in 1969. He earned a Ph.D. (Thse d'tat) in computer science at the University of Grenoble in 1977. Jean-Marie began work on the Cabri II project in 1981 as an environment for graph theory. He has devoted his research efforts to the use of geometric methods for the study of different classes of graphs, especially hypercubes. Franck Bellemain earned a Ph.D. in mathematics at the Universit Joseph Fourier in 1992. He began work on the Cabri II project in 1986 and is responsible for writing several versions of the software for Macintosh, PC-compatible, and Japanese computers. His research and thesis have been devoted to the use of technology in the classroom.
Cabri Geometry II Features
Includes interactive analytic, transformational, and Euclidean geometry. Allows intuitive construction of points, lines, triangles, polygons, circles, and other basic objects. Translates, dilates, and rotates geometric objects around geometric centers or specified points plus reflection, symmetry, and inverse of the objects. Constructs conics easily, including ellipses and hyperbolas. Explores advanced concepts in projective and hyperbolic geometry. Annotates and measures figures (with automatic updating). Uses both Cartesian and polar coordinates. Provides for user display of the equations of geometric objects, including lines, circles, ellipses, and coordinates of points. Allows the user to create macros for frequently repeated constructions. Lets the teacher configure tool menus to focus student activities. Checks geometric properties to test hypotheses based on Euclids five postulates. Hides objects used in constructions to reduce screen clutter. Differentiates objects through the use of paint-like color and line palettes. Computes a locus continuously. Illustrates the dynamic characteristics of figures through animation. Allows the user to save drawings and macros to disk. Opens geometry constructions created on the TI-92. Provides one square meter of full-size work space, and prints the 8.5 by 11.0 inches (21.59 by 27.94 cm) drawing area.

Copying permitted provided TI copyright notice is included 1997, 1999 Texas Instruments Incorporated
Copying permitted provided TI copyright notice is included 1997, 1999 Texas Instruments Incorporated.
Getting Started with Cabri Geometry II
Getting the Most from Getting Started
About the Getting Started Guide
The Getting Started guide introduces you to Cabri Geometry II with hands-on exercises. However, it does not cover all features of Cabri II, nor does it demonstrate all the ways to construct any particular object. Getting Started includes the following sections:

First Steps

This section provides system requirements and installation instructions for Cabri Geometry II and briefly discusses the Cabri Geometry II tools. Checking System Requirements. Describes requirements for Windows, DOS, and Macintosh systems... 6 Installing Cabri Geometry II. Explains how to install Cabri Geometry II.. 6 Starting Cabri Geometry II. Explains how to start Cabri Geometry II.. 7 Cabri Geometry II Desktop. Briefly describes the Cabri Geometry II screen and toolbar. 8 Quick Reference Sheet. Gives a list of the tools under each toolbox in the Cabri Geometry II toolbar... 9

Basic Operations

This section provides step-by-step exercises that give you hands-on experience with several features basic to the construction of geometric objects using Cabri Geometry II. To quickly learn Cabri Geometry II, complete these four exercises. Modeling: Handshakes. Use a circle, points, and line segments to model a real-world problem for pattern recognition.. 11 Exploring: Transformations in the Coordinate Plane. Construct a triangle, and explore reflection, rotation, and dilation around the x and y axes.. 18 Exploring: Power (Steiner) of a Point Problem. Construct a point as described by Euclid, and then move the point to calculate various powers and record them in a table. 25 Constructing a Macro: Pentagram. Create a pentagram by inscribing pentagons to illustrate some important features of macros.. 32
Menu Options and Toolbar Commands
Menu Options. Provides a quick reference and brief description of the menu options. 38 Toolbar Commands. Provides a quick reference to the tools available on each toolbar and a brief description about the operation of each tool. 40

Note: Cabri Geometry II is supplied on high-density diskettes. If your computer will not accept these diskettes, call, 1-800-TI-CARES and a service representative will supply you with low density diskettes.
Installing Cabri Geometry II on a network (continued)
Macintosh and DOS 1. Install Cabri Geometry II on the network server using the instructions given on the previous page. 2. Run the program from the server the first time, and enter the requested information. 3. To run Cabri Geometry II on each network client, go to the directory on the network server where the Cabri Geometry II application is installed. Macintosh users may double-click on the Cabri II icon; DOS users may run Cabri2.exe to start the program. The procedure described below, for Windows users, allows multiple client computers to run Cabri Geometry II using the application software installed on the network server. Each client computer is provided with the necessary system files to run Cabri Geometry II and a shortcut icon that is linked to the application file on the network server. Windows 3.1 and Windows 95 1. Install Cabri Geometry II on the network server using the instructions given on the previous page. In the Select Destination screen, you must select a directory that will be accessible from each client computer on the network. 2. Temporarily copy setup.exe and setup.w02 from the installation diskettes to the same directory in which you installed Cabri Geometry II in step 1. 3. On each network client, go to the directory on the network server that contains setup.exe and double-click to on this file to run the setup program. 4. In the Select Destination Directory screen, click on the Browse button and select the same directory that you used in step 1. Make sure the correct directory is displayed at the top of the window. You may edit the path, if necessary, and then click on OK. Ignore the message that the directory already exists. 5. In the Select Components screen, deselect the first three components. The installation program will determine if the fourth component is necessary for Windows 3.1x users. 6. When Cabri Geometry II has been installed on all client computers, delete the two files that were temporarily copied to the network server in step 2.
Starting Cabri Geometry II
Macintosh You can use one of four methods to start the software on a Macintosh: Use Open in the Finder. Double-click on the Cabri II icon. Double-click on any Cabri Geometry II construction file, tool configuration file, or macro file. Drag and drop any construction file onto the Cabri II icon (System 7 users only). Windows Double-click on the Cabri II icon. DOS Type CABRI and press ENTER from the DOS prompt directory where the Cabri Geometry II files are located. (Optional) Add the Cabri directory to your DOS path to open Cabri Geometry II from any directory.

Modeling: Handshakes (Continued)
Move and resize the circle
6. Instead of making another circle, practice moving and resizing the circle. The tools for moving and resizing are in the Pointer toolbox, which is the first toolbox on the toolbar. Begin by pulling down the Pointer toolbox; then point to and select the Pointer tool ("). Move the " into the drawing window. Notice that the " changes to a ! (cross hair). Move the ! to the point at the center of the circle. It changes to a $ (pointing hand) and the message This point appears. Cabri Geometry II recognizes all the objects you create and informs you when the cursor is close enough to an object for you to select it or perform some other activity. Click once on the mouse button. The point flashes, indicating that the point is selected. 8. Click and hold the mouse button. The $ changes to a % (grasping hand) to show that you can move the object. While holding the mouse button down, drag the point toward the right to move the circle. Release the mouse button. (Note: You dont have to select a point to move it.)

This point

Now move the $ away from the center point. It changes back into a !. Move the ! toward the circumference until it changes to the $ with the message This circle. Click once on the mouse button. (Do not hold the mouse button down.) The circumference appears to be moving or flashing. This marquee outline indicates that the circumference is selected. To deselect the circle, move the $ until it changes to a ! and then click. The circumference no longer appears to be moving.
10. Move the ! near the circumference until the $ appears. Click and hold the mouse button. The $ changes into a %. Enlarge the circle to fill the screen by dragging the circumference. Release the button.
Construct points to represent the four friends
11. The second button on the toolbar shows the currently selected tool in the Points toolbox. Pull down the Points menu and select the Point tool.
12. Pull down the Options menu above the toolbar. Select Show Attributes (Macintosh, Windows) Hide/Show Attributes (DOS).
Macintosh and Windows only
The attribute icons appear vertically on the left side of the drawing screen. These icons represent tools that let you control the appearance of objects that you create.
13. The fourth attribute icon represents the currently selected Point attribute. Click and hold the button to display the choices. You can construct a point as a , , , , or. Select the attribute. Now every point that you construct with the Point tool will appear on the drawing screen as a until you change the attribute. 14. Move the # toward the circumference until the pencil changes appearance and the message On this circle appears. This message tells you that the defined point will be attached to the circle and that, if you move the circle, the point will move with it. Click to create a to represent the first friend. 15. Add the other three friends in the same way, evenly spaced around the circle. To check your work, complete the Checkpoint #1 instructions on the next page.

Checkpoint #2: Check to see that you have not inadvertently created new points as the end points of the line segments. a. Select the Pointer tool (") from the Pointer toolbox (first button).
b. Drag one of the points on the circle about one-half of an inch (1.3 cm). The point (and its associated label) should move around the circumference, moving all of its line segments with it. c. Repeat for the other points.
Note: If the cursor changes to a magnifying glass and the message Which object? appears, you may have created duplicate points and one or more line segments are not attached to an original point. To start over, press COMMAND+A (Macintosh) or CTRL+A (Windows, DOS) on your keyboard to select all objects on the screen, and then press DELETE. A clean drawing window appears. Repeat the exercise. It will go very quickly now that you are familiar with the Cabri Geometry II tools!
Count and record the handshakes
21. To keep track of each handshake as you count it, use the selection feature. Click on the first line, and then press and hold SHIFT as you click on each additional line. The change in appearance of each line helps you keep track as you count. Enter the number in the chart at the beginning of the exercise. Click outside the circle to deselect the lines.
Open the on-screen attribute palette
22. You can help differentiate new points and handshakes from the old points and handshakes by using the color, point, and line attributes. For convenience, you can create a customized on-screen attribute palette of the attribute icons. Click and hold on the Color Attribute toolbox (the top button on the attribute toolbar); however, instead of selecting a color when the palette opens, hold down the mouse button and drag the entire palette onto the drawing window. Release the mouse button. Click on each of the attribute buttons on the vertical attribute toolbar to add the tools to the on-screen attribute palette. These include color, line thickness, line appearance, point type, and others. Note: On monochrome systems, the color palette is not available. On these systems, the palette presents varied shades of gray. You can drag the palette by its title bar to a more convenient location on the drawing window. You can close any unneeded attribute toolbox by clicking on the close box at the left corner of that toolbox.
Add the fifth friend and handshakes
23. Select the Point tool from the Points toolbox (second button). Notice that and the color red are selected on the palette. (Each time you select a new tool, the palette shows the current settings for that tool.) 24. Select a different color and x as the Point Attributes for the fifth friend. Then add the new friend to the circle. Select Label from the Display toolbox (tenth button). Move to the new point, click once, and type the friends name. You can use the Pointer tool (first button) to enlarge the circle and reposition the points and labels as needed for visibility. Note: You can label a point when you create it by typing the name on the keyboard immediately after creating the point. However, this labeling method is limited to five characters. 25. Select the Segment tool from the Lines toolbox (third button). Choose a different color and a different Line Attribute, such as a dotted line or a heavier weight. Add the new handshakes. (Remember to click only when the message says This point so that you dont create a new point.) Count the handshakes, and enter the results on the chart at the beginning of the exercise.

Construct a polygon

19. Open a new drawing by selecting New from the File menu. 20. Display the coordinate system by selecting the Show Axes tool from the Draw toolbox (last button). 21. Select the Polygon tool from the Lines toolbox (third button). Construct a four-sided polygon in the upper right quadrant by moving the # and clicking once at each vertex. Make it any shape you want. The last vertex must be the same as the first. Click when the message This point appears.

Translate the polygon

22. You can translate an object according to a selected vector. Select Vector from the Lines toolbox (third button). Move the # and click once in the upper right quadrant to create the tail of the vector, and move the # and click again to create the head of the vector.
23. Select the Translation tool from the Transform toolbox (sixth button). Click on the polygon when the message Translate this polygon appears, and then click on the vector when the message by this vector appears. The translated polygon appears, offset from the original polygon by the direction and length (magnitude) of the vector.
24. Drag the head of the vector when the cursor changes to $ and the message Translate this point appears. The translated polygon follows the head of the vector.
25. Using the Pointer tool from the Pointer toolbox (first button), drag the original polygon. What happens to the translated polygon?
Rotate a polygon by a defined angular value.
26. You can rotate a polygon by an angular value that you define. This example begins with the value 30. First, remove the polygons created previously. To do this, select the Pointer tool from the Pointer toolbox (first button). Then press and hold the mouse button in a blank area outside the polygons and vector. Drag the mouse across the drawing until a marquee rectangle surrounds all of the objects. Release the mouse button. All of the objects in the rectangle are selected (except the axes, which cannot be removed in this manner). Press DELETE on your keyboard. The objects are removed. 27. Select the Polygon tool from the Lines toolbox (third button). Construct a four-sided polygon in the upper right quadrant. Make it any shape you want. 28. Select the Numerical Edit tool from the Display toolbox (tenth button). Click at the location where you would like to place the numerical value (you can place it anywhere in the quadrant). A numerical edit window appears.
29. Type the value 30 in the numerical edit window. Then, press U (Macintosh) or CTRL+U (Windows, DOS). A list of units appears in a pop-up menu. Select the unit Degree. The degree symbol () is assigned to the value 30.

30. Select the Rotation tool from the Transform toolbox (sixth button). Move the # toward the polygon until the message Rotate this polygon appears. Click to select the polygon. 31. Move the # toward the origin point until the message around this point appears. Click to select this point. Now move the # toward the value 30 until the message using this angle appears. Click to select the value. An image of the polygon that is rotated 30 degrees around the origin point is created.
Dynamically change the rotation angle.
32. Select the Numerical Edit tool from the Display toolbox (tenth button). Move the I (I-beam) towards the value 30 degrees until the message This number appears. Click once to select the value. A flashing cursor appears in the window next to the number. 33. Press the ! (left arrow key) on your keyboard to position the flashing cursor to the right of the 3. Now press the # (up arrow key). Notice that the first digit increases by 1. (The Numerical Edit tool increases/decreases the digit to its left when the up and down arrow keys are used.) Press the # (up arrow key) until the value reads 90 degrees, noticing the changes in the rotated polygon. Now, press the $ (down arrow key). The digit decreases by 1. You can change the rotation angle dynamically to any value using this method. Alternatively, you can highlight the value using the mouse and type in a new value.
Dilate the polygon by a defined factor.
34. You also can dilate a polygon by a factor that you define. This example begins with the factor 1.2. Select the Numerical Edit tool from the Display toolbox (tenth button), if necessary. Click at the location where you would like to place the numerical value (you can place it anywhere in the quadrant). A numerical edit window appears. 35. Type the value 1.2 in the numerical edit window. Then press U (Macintosh) or CTRL+U (Windows, DOS) to see the list of units. Select the option Without unit. No unit is assigned to the value.
Dilate the polygon by a defined factor (continued)
36. Select the Dilation tool from the Transform toolbox (sixth button). Move the # toward the original polygon until the message Dilate this polygon appears. Click to select the polygon. 37. Move the # toward the origin point until the message with respect to this point appears. Click to select the point. Now move the # toward the value 1.2 until the message using this factor appears. Click to select the value. An image of the polygon that is dilated by the factor 1.2 with respect to the origin point is created.

Exploring: Power (Steiner) of a Point Problem (Continued)
Modify the appearance of the construction
5. Select the Modify Appearance tool from the Draw toolbox (last button). A pop-up screen showing the various appearance attributes appears. Click on the large, solid point in the top row. If necessary, point to the top line of the pop-up screen and hold down the mouse button to drag the pop-up screen away from your drawing. 6. Move the ! toward point S until the ! changes to a 2 and the message This point appears. Click once. The point changes to a large point. Repeat this procedure for the two independent points. 7. Click on the close box in the top left corner of the pop-up screen to remove the screen from the drawing window.
Construct segments within the circle
8. Select the Segment tool from the Lines toolbox (third button). Move the # toward one of the independent points on the circle until the message This point appears. Click once. The initial end point of the segment appears. Move the # toward point S until the message This point appears. Click to complete the segment construction. Repeat this procedure to construct a segment on the other line. 9. Move the # toward point S until the message This point appears. Click once to create the initial end point of the segment. Move the # toward one of the intersections of line and circle until the message Point at this intersection appears. Click to complete the segment construction. Repeat this procedure to construct a segment on the other line.
Point at this intersection

Label the points

10. Select the Label tool from the Display toolbox (tenth button). Move the ! toward one of large points on the circle until the ! changes to I (I-beam) and the message This point appears. Click once. An edit window appears next to the point. Enter the label from the keyboard. Call this point A. Move the I toward the small point which is on the same line. Click once to open the edit window. Call this point B. 11. Repeat step 10 for the two unlabelled points on the circle, labeling them C and D.

Divide the segment into eighths
3. Select the Midpoint tool from the Construct toolbox (fifth button). Move the # toward the segment until the $ and the message Midpoint of this segment appear. Click once. The midpoint of the segment appears. The segment is divided into halves. 4. To divide the segment into eighths, you need to divide the segment into two more halves. That is, 1/2 * 1/2 * 1/2 = 1/8. Use the Midpoint tool to perform the division. Move the # toward the midpoint until the $ and the message Midpoint between this point appear. Click once. Move the # toward the end point on the right until the $ and the message and this point appear. Click once. The midpoint between the two selected points appears. The segment has a one-quarter division. Divide the right-most quarter again using the Midpoint tool. The segment now has a one-eighth division.
Define a macro to perform a segment division
To build a pentagonal curve of pursuit you need to find a point on each side of a regular pentagon that is one-eighth the distance of that side. The segment division performed in the previous steps shows the procedure you need to accomplish the task. Macros are used to perform repetitive tasks or to create unique objects. Since building a pentagonal curve of pursuit is a repetitive task, it would be beneficial to create a macro that would perform the task. To create a macro, you first must select initial object(s) that are used to define the final object(s). The next step is to select the final object(s) and then, if necessary, to change the attributes of the object(s) as they will appear in the final construction. The final step is to define the macro for inclusion in the Macro toolbox. The macro is then available for use.
Select the segment as the initial object
5. Select Initial Object from the Macro toolbox (seventh button). Move the ! toward the segment until the message This segment appears. Click to select the segment as the initial object. The segment appears to be moving or flashing (a marquee outline), indicating that it is selected.
Select the point that is one-eighth the length of the segment as the final object
6. Select Final Object from the Macro toolbox. Move the ! toward the second point from the right on the segment until the message This point appears. Click to select this point as the final object. The point flashes. You are now ready to define the macro. Select the Define Macro tool from the Macro toolbox. A dialogue box appears in which you can name your macro. (Macintosh) Enter the name Segment Division from the keyboard in the field Name of the construction:. Notice that the letter in the icon font: field changes to S. This letter will appear as an icon in the Macro toolbox identifying the Segment Division macro. (Windows, DOS) Overwrite the default name New construction and enter the name Segment Division from your keyboard in the field labeled Name of the construction:. It is not necessary to save the macro to a file in this case since it is an intermediate step in the construction of the pentagonal curve of pursuit. However, if you wish to save the macro to a unique file on disk, click on the Save to file box to mark it with an Q. This is your only opportunity to save the macro to an independent file, although it will be saved automatically with the construction. Macintosh

Continue to apply the Pentagram macro
25. Apply the macro Pentagram to the construction again. Point to the new inner pentagon and click to create yet another pentagon. Repeat until you have a construction similar to the illustration. Note: As your construction gets more and more crowded, you can rely on the ambiguity feature of Cabri II to select the pentagon created last. That is, the * pointer may appear along with the message Which object? Press and hold the mouse to see a list of the objects available. Point to the last object in the list, which is the last object created, and release the mouse to select it. Your computers response will become slower as more objects are added to the construction.

Optional macros

It is also possible to combine more steps in a macro. For example, create four inscribed pentagons, select the original pentagon as the initial object, select the remaining pentagons as the final objects. The macro then will generate four inscribed pentagons.

Other line designs

Try using this technique to construct other line designs. This example was inspired by Dale Seymours book Introduction to Line Designs published by Dale Seymour Publications.

Menu Options

Ctrl+N Ctrl+O Ctrl+S New Open. Save Save as. Revert. Ctrl+P Show Drawing. Page Setup. (Macintosh, Windows) Printer Setup. (DOS) Print. Ctrl+Q Quit Open a new Cabri Geometry II drawing. Open a saved Cabri Geometry II drawing. Save the current Cabri Geometry II drawing in the file from which it was loaded. Save the current Cabri Geometry II drawing to a specified file. Replace the current drawing with the most recently saved version. Zoom out to the one-square meter drawing sheet; reposition the window. Select printer and page options.
Print the current page (Macintosh, Windows, DOS) or the entire drawing area (Macintosh only). Close Cabri Geometry II.
Ctrl+Z Ctrl+X Ctrl+C Ctrl+V Undo Cut Copy Paste Clear Ctrl+A Select all Replay Construction Ctrl+F Refresh Drawing Undo the last action. Remove the selected object(s) from the drawing to the clipboard. Copy the selected object(s) from the drawing to the clipboard. Paste the clipboard contents into the current drawing. Clear (erase, delete) all selected items. Select all objects in the drawing. Replays each step of a construction. Refresh the drawing screen; remove leftover Trace elements.

Options

Hide/Show Attributes Preferences. Tool Configuration. Hide the toolbar or display the toolbar that controls how objects look. Set preferences for how drawings are set up. Rearrange or hide tools.

A (Macintosh) Help (Windows, DOS) About. Displays a description of the selected toolbar icon in the Help window at the bottom of the Cabri Geometry II screen. Displays information about Cabri Geometry II that includes the authors names, copyright notice, and the version number of the software.

Helpful Shortcuts

Press + or Press Shift Press Tab Press Enter To increase or decrease the displayed precision in Numerical Edit. To increase or decrease the animation speed in Animation or Multiple Animation. To increase or decrease the number of objects in the selected locus. To limit the slope of lines, rays, segments, vectors, triangles, polygons, or axes to increments of 15. To limit the radius to multiples of 1 cm when creating circles. To select multiple objects. To record new values in a table. To change the format of a selected equation.
To start a Multiple Animation.
Press and hold the mouse key To display all directly moveable (basic and independent) objects as flashing. The cursor must be in an unoccupied space. Press Ctrl and drag the mouse To scroll the drawing window. Double-click the mouse key Click the mouse key Ctrl+U On a label, comment, numerical value, or table to invoke the appropriate editor. Anywhere in the gray area of the Toolbar to access the Pointer tool. Displays list of units in a pop-up menu when the Numerical Edit tool is selected.

Toolbar Commands

Pointer
Pointer Rotate Dilate Rotate and Dilate Select, move, and manipulate objects. Rotate an object around a selected point or the objects geometric center. Expand or contract an object around a selected point or the objects geometric center. Simultaneously rotate and dilate an object around a selected point or the objects geometric center.

Points

Point Point on Object Construct a point defined in free space, on an object, or at the intersection of two objects. Construct a point defined on an object.
Intersection Point(s) Construct a point at each intersection of two selected objects.
Line Segment Ray Vector Triangle Polygon Regular Polygon Construct an infinite line through a point at a slope (specified by clicking a second time in free space or at a point). Construct a segment, defined by two end points, which may be created or defined in free space or on a defined object. Construct a ray, defined by an end point and direction, extending infinitely. Construct a vector with magnitude and direction defined by two points. Construct a triangle, defined by three points (vertices), which may be created or defined in free space or on a defined object. Construct an n-sided polygon; the last point must coincide with the beginning point. Select or create a point for each vertex. Construct an n-sided regular polygon. Click for center and radius, move clockwise (convex) or counterclockwise (star) to set n (30).

Color Palette

Angle Mark
1 tick mark 2 tick marks 3 tick marks

Line Thickness

Light lines Medium lines Thick lines

Segment Mark

No tick mark 1 tick mark 2 tick marks 3 tick marks

Line Appearance

Solid lines Dotted lines Dashed lines
Cartesian & Polar Coordinates
Cartesian coordinates Polar coordinates measured in degrees Polar coordinates measured in grads

Point Types

Small point Medium point Large point Hollow point Crosspoint Cross
Polar coordinates measured in radians

Text Appearance

Plain Colored background In box In colored box