Texas instruments CABRI GEOMETRY II Guidebook

CABRI GEOMETRYë II

Guidebook for Macintoshë, Windowsë, and MS-DOS

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For more information about TI products and services, contact TI by e-mail or visit the TI calculator home page on the world-wide web.

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Cabri Geometry II is a trademark of Université Joseph Fourier. Macintosh is a registered trademark of Apple Computer Corporation Incorporated. MS-DOS and Windows are registered trademarks of Microsoft Corporation. PostScript is a registered trademark of Adobe Systems Incorporated.

CABRI GEOMETRY II

Guidebook for Macintosh

and MS-DOS

, Windowsë,

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 Mathématiques Appliquées de Grenoble (IMAG), a research lab at the Université 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 conjecturing—from simple shapes to advanced projective and hyperbolic geometry.

About the Developers

Jean-Marie Laborde is founder and Research Director of Laboratoire de Structures Discrètes et de Didactique (LSD2), a research laboratory within IMAG. He graduated in mathematics at Ècole Normale Supérieure in Paris in 1969. He earned a Ph.D. (Thèse d'État) 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 Université 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 Euclid’s 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

About this Guidebook

CHAPTER 1: LEARNING THE BASICS

First Steps Constructing Objects

.............................................................................

CHAPTER 2: USING THE MENUS

File Menu Edit Menu Options Menu Help Menu

.............................................................................

..........................................................................

.............................................................................

..................................................................

.............................................

...................................................................

...................................................

CHAPTER 3: USING THE POINTER TOOLBOX

Pointer Rotate Dilate Rotate and Dilate

CHAPTER 4: USING THE POINTS TOOLBOX

................................................................................

.................................................................................

.......................................................................

......................................

....................................

1–1

1–2

1–10

2–1

2–2 2–5 2–7

2–12

3–1

3–2 3–3 3–4 3–5

4–1

..................................................................................

Point Point on Object Intersection Point(s)

CHAPTER 5: USING THE LINES TOOLBOX

..................................................................................

Line Segment Ray Vector Triangle Polygon Regular Polygon

...............................................................................

...................................................................................

................................................................................

...............................................................................

........................................................................

...................................................................

........................................

.......................................................................

CHAPTER 6: USING THE CURVES TOOLBOX

.................................................................................

Circle

...................................................................................

Arc

.................................................................................

Conic

.....................................

4–2 4–3 4–4

5–1

5–2 5–4 5–5 5–6 5–7 5–8 5–9

6–1

6–2 6–3 6–4

iii

CHAPTER 7: USING THE CONSTRUCT TOOLBOX

...............................

7–1

Perpendicular Line Parallel Line Midpoint

..............................................................................

Perpendicular Bisector Angle Bisector Vector Sum Compass

............................................................................

..............................................................................

Measurement Transfer

.................................................................................

Locus Redefine Point Redefine Object

.....................................................................

...........................................................................

..................................................................

.........................................................................

..................................................................

.........................................................................

........................................................................

CHAPTER 8: USING THE TRANSFORM TOOLBOX

Reflection Symmetry Translation Rotation Dilation Inverse

CHAPTER 9: USING THE MACRO TOOLBOX

.............................................................................

............................................................................

...............................................................................

................................................................................

.....................................

...............................

7–2 7–3 7–4 7–5 7–6 7–7 7–8

7–9 7–11 7–13 7–14

8–1

8–2

8–3

8–4

8–5

8–6

8–7

9–1

How to create a macro Initial Object Final Object Define Macro

...........................................................................

..........................................................................

..................................................................

CHAPTER 10: USING THE CHECK PROPERTY TOOLBOX

Collinear Parallel Perpendicular Equidistant Member

..............................................................................

...............................................................................

..........................................................................

............................................................................

...............................................................................

......................

9–2

9–3

9–4

9–5

10–1

10–2 10–3 10–4 10–5 10–6

Copying permitted provided TI copyright notice is included

Table of Contents

(continued)

CHAPTER 11: USING THE MEASURE TOOLBOX

Distance & Length

..................................................................................

Area

.................................................................................

Slope

.................................................................................

Angle Equation & Coordinates Calculate Tabulate

..............................................................................

......................................................................

.................................................................

CHAPTER 12: USING THE DISPLAY TOOLBOX

.................................................................................

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

.............................................................................

.........................................................................

............................................................................

...............................................................................

...........................................................................

.............................................................................

.....................................................................

.................................

...................................

11–1

11–2 11–3 11–4 11–5 11–6 11–7

11–11

12–1

12–2 12–3 12–5 12–7 12–8 12–9

12–10 12–11

CHAPTER 13: USING THE DRAW TOOLBOX

Hide/Show Color

...................................................................................

Fill Thick Dotted Modify Appearance Show/Hide Axes New Axes Define Grid

INDEX

.............................................................................

............................................................................

.................................................................................

................................................................................

.....................................................................

.......................................................................

.............................................................................

.....................................................................................................

......................................

INDEX–1

13–1

13–2 13–3 13–4 13–5 13–6 13–7 13–8 13–9

13–10

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 Windowsé and MS-DOSë-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.

4 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.

4 Key names are shown in small capital letters such as

Escape key. The the same function. In this guidebook, “Press

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.

4 Chapter 2 describes the Cabri II menus and provides step-by-step procedures for using them.

4 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 When used as an instruction, point means to place the screen pointer on

click Click means to press and release the mouse button quickly, usually when

double-click Double-click means to click the mouse button twice in succession.

RETURN

key on the Macintosh and the

ENTER

top of the object you wish to select.

pointing to a specific location

CTRL

for the Control key and

ENTER

key on the PC keyboard perform

” means to press either

ENTER

ESC

for the

RETURN

drag 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.

modify When used as an instruction, modify means to change the appearance,

size, location, or orientation of the object.

marquee outline Marquee outline is the outline of an object in animated dots, similar to a

movie marquee.

marquee rectangle Marquee rectangle is the selection rectangle that appears when you drag

Pointer

with the

tool from an unoccupied location in the drawing window. When you release the mouse button, objects that lie completely within the rectangle are selected.

Copying permitted provided TI copyright notice is included

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 CONSTRUCTING OBJECTS

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

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

Chapter 1: Learning the Basics 1-1

First Steps

Checking system requirements

Macintosh DOS

¦ Macintosh Classic or better.

¦ System 6.0 or later.

¦ 1 Mb available RAM for a Macintosh

Classic. (Memory requirements will be greater for color or larger monitors than on the Classic.)

¦ Hard disk with 1.2 Mb available for

program and demonstration files.

Windows 3.1 Windows 95

¦ 386 PC or better required; 486DX

recommended.

¦ PC must be in 386-Enhanced mode with

Virtual Memory enabled.

¦ VGA, SVGA video adapter and a color

monitor.

¦ 6 Mb RAM (minimum) memory installed.

¦ 7 Mb available hard disk space for program,

demonstration files, and system extensions.

¦ Mouse, or an equivalent pointing device.

¦ DOS-compatible computers (PCs), 386 or

better, and running MS-DOS 3.3 or later.

¦ EGA, VGA, SVGA video adapter and a color

monitor.

¦ 3 Mb RAM (minimum) memory installed.

¦ Hard disk with 2.5 Mb available for

program and demonstration files.

¦ Mouse, or an equivalent pointing device.

¦ 386 PC or better required; 486DX

recommended.

¦ VGA, SVGA video adapter and a color

monitor.

¦ 6 Mb RAM (minimum) memory installed.

¦ 2 Mb available hard disk space for program

and demonstration files.

¦ Mouse, or an equivalent pointing device.

Installing Cabri Geometry II

Macintosh DOS

1. Create a folder named disk.

2. Insert the Cabri Geometry II Macintosh diskette in your floppy disk drive.

3. Double-click on the and follow the directions on the screen.

Windows 3.1 Windows 95

1. Insert the Cabri Geometry II for Windows diskette #1 in your floppy disk drive.

2. From Program Manager, click on

A:\SETUP

enter prompts.

, and then follow the screen

Cabri II

Installer

on your hard

on the diskette

RUN

and

1. Insert the Cabri Geometry II DOS diskette in your floppy disk drive.

2. At the DOS prompt, enter:

A:\INSTALL

follow the screen prompts.

1. Insert the Cabri Geometry II for Windows diskette #1 in your floppy disk drive.

2. Click on and then follow the screen prompts.

START/RUN

B:\INSTALL

and enter

, and then

A:\SETUP

Installing Cabri Geometry II on a network

If you have purchased the network license for Cabri Geometry II, you may run the software on your network. Use network procedures that are compatible with your network to install Cabri Geometry II. See your Macintosh, Windows, or DOS User’s manual or your network documentation for more information, if necessary.

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.

1-2 Chapter 1: Learning the Basics

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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

. 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 DOS

You can use one of four methods to start the software on a Macintosh:

¦ Use

Open

¦ Double-click on the

¦ Double-click on any Cabri Geometry II

construction file, tool configuration file, or macro file.

¦ Drag and drop any construction file onto

Cabri II

the

Windows

Double-click on the

Finder

in the

Cabri II

icon.

icon (System 7 users only).

Cabri II

icon.

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.

Chapter 1: Learning the Basics 1-3

First Steps

(Continued)

Optimizing your Macintosh system configuration

If you are starting Cabri Geometry II on a Macintosh for the first time, you may need to make some adjustments to make Cabri Geometry II compatible with your Macintosh computer system configuration.

Graphics intensive programs require a large amount of memory to operate. The amount of memory required directly relates to the size of your monitor and to the number of colors chosen to represent graphical elements. Cabri Geometry II may require more memory than other applications due to its interactive nature. Cabri Geometry II can assist you in optimizing your system.

If you see a warning message from the configuration. This message indicates the amount of memory needed to run Cabri Geometry II efficiently on your computer with your current configuration.

Click the windows that are currently open. This frees the memory that these applications are using.

To change the amount of memory allocated to Cabri Geometry II, first make sure the selected. Then, from the decrease the application memory size to a value that is compatible with your computer.

Finder

, you need to make some adjustments to your system

button to proceed (Cabri Geometry II does not start). Then close any applications or

Cabri II

Finder

, select

Get Info

in the

File

menu. Once the

Get Info

window appears,

icon is

If you are using System 7, an optional method is to use

Virtual Memory

to increase the amount of

memory available to applications. See your Macintosh User’s manual for more information.

The previous dialog box indicates the amount of available memory on your computer. You may also select

About this Macintosh

in the

Apple

menu for the same information.

Changing your Macintosh system configuration using Cabri II

If you open Cabri Geometry II and the memory allocation on your Macintosh is not optimal, the following dialog box appears. We recommend that you allow Cabri Geometry II to select optimal

Manual

parameters for your system automatically or that you select them using the

You may wish to quit and modify the settings yourself if you are familiar with the memory and monitor control panels.

If you select the

Automatic

button, Cabri Geometry II computes the optimal settings for your computer and then quits. The number of colors may change in the process of optimizing your configuration. Double-click on the Cabri Geometry II icon for the changes to be applied to Cabri Geometry II.

button.

Manual

If you select the

button, Cabri Geometry II continues to the optimization dialog box (see example on the next page) that allows you to optimize your configuration as you want. Read the items in the

Current Settings

field first, and then manipulate the other fields as described below the example. (You can also access the following dialog box by pressing the the software.)

1-4 Chapter 1: Learning the Basics

OPTION

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key when starting

Status:

The status indicates whether or not Cabri Geometry II can run with the current settings.

# Screen Colors

Memory Setting

# Objects

# Colors

The number of colors used to display objects is directly related to the amount of memory required to execute Cabri Geometry II. You can click on the up or down arrow buttons in this field to change the number of

Status

screen colors. Check the acceptable. Click on

to continue.

field to determine if these values are

The amount of memory available and the number of colors displayed determine the number of objects that can be constructed. You can click on the up and down arrow buttons in this field to change the amount of memory allocated to Cabri Geometry II. The value on the left indicates the amount of memory required to run Cabri Geometry II on your computer in black and white. The value on the right indicates the amount of memory

Status

currently available on your computer. Check the

these values are acceptable. Click on

to continue.

field to determine if

The amount of memory available is directly related to the number of objects that can be constructed. Click on this button to optimize the number of objects that can be constructed. If memory is limited, Cabri Geometry II will probably suggest that fewer colors be used to construct more objects. For optimal performance, Cabri Geometry II attempts to allocate enough memory to construct at least 300 objects.

The number of colors used to display objects is directly related to the amount of memory required to execute Cabri Geometry II. Click on this button to optimize the number of colors displayed. If you use other applications regularly that require 256 colors, you may wish to optimize the number of colors. Given limited memory, this decreases the number of objects that you can construct.

Chapter 1: Learning the Basics 1-5

First Steps

(Continued)

The Cabri Geometry II window

The illustration below shows the Cabri Geometry II window. This window contains the essential elements of the Cabri Geometry II software. A description of each element follows the illustration.

Note: The screen shown below illustrates the Macintosh version. Screens on Windows and DOS systems are similar but slightly different.

Menu Bar

Close Box

Attribute Icons

Drawing Window

Help Icon

Toolbar

Zoom Box

Attribute Palette

This circle

Size Box

Help Window

Elements of the Cabri Geometry II window

Drawing Window Menu bar

1-6 Chapter 1: Learning the Basics

This region is where you build geometric constructions.

The menu bar contains common graphic user interface menus for file management and editing, together with Cabri Geometry II options.

Scroll Bars

Pointer Message Selection Pointer

Copying permitted provided TI copyright notice is included

Toolbar

The toolbar contains tools for building constructions. Eleven toolboxes reside on the toolbar (see illustration below). To access a toolbox, press and hold the mouse button on the icon. The items in that toolbox appear.

Pointer

Points

Lines

Curves

Construct

Transform

Macro

Check Propert

Measure

Displa

Draw

Attribute icons

Help Icon

(Macintosh)

Help menu option

(Windows, DOS)

Selection pointer

Close box

Zoom box

(Macintosh, Windows)

Size box

(Macintosh, Windows)

Scroll bars

(Macintosh, Windows)

The attribute icons are not displayed unless you select the command in the

Options

menu on the menu bar. These allow you to

Show Attributes

modify the appearance of objects. You can create an attribute palette (tear-off menu) by dragging an icon from the attribute icons to the drawing window.

Clicking on the help icon A creates a help window at the bottom of your screen that contains useful help messages for each command. Clicking on the A again removes the help window.

Clicking on the

Help

menu option and selecting

key toggles the help window ON and

OFF

Help

or pressing the

The selection pointer is the primary tool for selecting menus and building constructions. The shape of the pointer changes according to its current operation and location.

The close box closes the window and creates a dialog box that allows you to save your work if you have not done so.

The zoom box toggles the size of the window between the current size and the full screen size.

Dragging the size box to a new location resizes the drawing window.

Clicking in the scroll bars or on the scroll arrows moves the contents of the drawing window vertically or horizontally.

Chapter 1: Learning the Basics 1-7

First Steps

(Continued)

About menus and toolboxes

Operations are grouped by type in the pull-down menus located on the menu bar and on the toolbar. Once a tool is selected, it remains active until you select another tool. If the icon of the tool you want is shown on the toolbar, select it by clicking once on the icon. Commands in the menu bar must be selected each time they are used.

Descriptions of the Cabri Geometry II menus and toolboxes follow:

MENUS Apple

(Macintosh only)

File Edit

Options

Window (Windows)

Help

(Windows, DOS)

TOOLBOXES Tools for ... Pointer Points Lines Curves Construct

Apple menu items or the Cabri Geometry II logo screen.

Commands for opening, closing, saving, or printing constructions.

Commands for selecting or copying objects, refreshing the drawing window, or replaying constructions.

Commands for tool configurations, hide/show attributes, preferences, or setting software defaults (Macintosh only).

Standard Windows display options.

Help options.

Selecting or for free-hand transformations.

Constructing points.

Constructing linear objects.

Constructing circles, arcs, or conics.

Euclidean geometry constructions.

Transform Macro Check Property Measure Display Draw

1-8 Chapter 1: Learning the Basics

Transformational geometry.

Making macros. New macros become part of this toolbox.

Checking properties of constructions based on Euclidean geometry.

Measurements or calculations.

Annotating your constructions or animating objects.

Changing the appearance of objects or displaying the coordinate system.

Copying permitted provided TI copyright notice is included

Accessing on-line help

Macintosh DOS

¦ Access on-line help by clicking on the help

icon A in the menu bar of the Cabri Geometry II drawing window.

¦ A window appears at the bottom of your

drawing that contains information about the tool currently selected.

¦ Select additional tools to see their help

information.

¦ Remove the help window by clicking on

the help icon again or by clicking on the close box in the help window.

¦ The close box appears when you click in

the help window.

Windows

¦ Access on-line help by clicking on the

Help menu option in the menu bar of the Cabri Geometry II drawing window and

Help

selecting

¦ A window appears at the bottom of your

drawing that contains information about the tool currently selected.

¦ Access on-line help by clicking on the

Help menu option in the menu bar of the Cabri Geometry II drawing window and selecting

Help

, or press F1.

¦ A window appears at the bottom of your

drawing that contains information about the tool currently selected.

¦ Select additional tools to see their help

information.

¦ Remove the help window by clicking on

the help icon again or by pressing

¦ Select additional tools to see their help

information.

¦ Remove the help window by clicking on

the help icon again.

Chapter 1: Learning the Basics 1-9

Constructing Objects

Pointers that guide you

Several types of pointers exist to help guide you through your constructions. The pointers are illustrated below.

Pointer Cursor looks like... arrow

cross hair construction pencil selection pencil

pointing hand selection hand

dragging hand open hand

grasping hand

magnifying glass I-beam paint brush

$ &

(

)

# '

The pointer is in the toolbar, menu bar, or scroll bars.

Pointer

The

A construction tool is active.

A construction tool is active and a point can be placed on an object.

A point can be selected.

An object is dependent or to show the intermediate stage between selecting an object and dragging.

An object can be moved.

The (DOS) is pressed.

The window can be scrolled using the mouse.

An ambiguity exists.

Text or numbers can be entered or edited.

Color or attributes can be changed.

tool is active.

COMMAND

key (Macintosh) or the

CTRL

paint bucket

crossed lines column width

4 3

An object can be filled with a pattern or color.

Comment

The

The column width of the table can be adjusted.

option is active.

Creating and selecting point*s

All objects are constructed using one or more points. You create or select points when a tool is active. In general, the order of operation is to select a construction tool from the toolbox, and then to create or select the required points that define the tool.

A point is created by a single click of the mouse. You can create points in unoccupied space when

construction pencil

the two objects when a cursor message appears and the pointer changes to the The following examples illustrate how to create and select points.

# cursor is visible. You can create a point on an object or at the intersection of

selection pencil

' cursor.

1-10 Chapter 1: Learning the Basics

Copying permitted provided TI copyright notice is included

Example 1: Creating the perpendicular bisector of two points

1. Select the

Perpendicular Bisector

tool from the

Construct

toolbox.

2. Move the # to any place in the drawing window and click

(not hold down) once.

A flashing point appears on the window, indicating that this point has been selected for the construction.

3. Move to another place and click again.

A second point appears as well as the perpendicular bisector of the segment connecting these two points. (Note: The segment does not appear.)

If the pointer is near a valid object, a cursor message is displayed. In some cases, it is sufficient to select only one object to define a construction, as the next example demonstrates.

Example 2: Creating the perpendicular bisector of a side of a triangle

1. Select

Triangle

from the

Lines

toolbox.

2. Move the # to any place in the drawing window and

click. Move to a second location and click, and then to a third location and click.

A triangle appears in the drawing window with the three points selected as vertices.

Note: Depending on the speed at which you constructed these three points, the sides of the triangle might appear during the construction. Try doing this slowly and watch the triangle materialize.

3. Select

Perpendicular Bisector

from the

Construct

toolbox.

Chapter 1: Learning the Basics 1-11

Constructing Objects

(Continued)

4. Move the cursor as follows so that the message

Perpendicular bisector of this side of the triangle

When the cursor is in unoccupied space in the drawing window, the # appears. Move the cursor near a side of the triangle. The cursor changes from the # to the $ with the message

Perpendicular bisector of this side of the triangle

(If the cursor is near a vertex of the triangle, the cursor message

This point

appears.)

Click once, and the perpendicular bisector of the side of the triangle appears.

Handling ambiguities

appears.

Perpendicular bisector of this side of the triangle

When two or more objects simultaneously occur at the location of the pointer, the * cursor and the cursor message

Which object?

appear. Press and hold down the mouse to see the

magnifying glass

options in a dialog box. Select an object by pointing to the appropriate choice in the box and releasing the mouse.

When multiple objects are present, they are listed in the order in which they were created. Selecting an object causes it to display in marquee outline. You can move (drag) it to a new

Pointer

location if it is an independent object and the

tool is selected. Click in unoccupied space to

deselect the object. If you are using a construction tool, the object is selected for the construction.

Determining dependent and independent objects

All objects are created using one or more points. The manner in which you create an object determines whether it is dependent or independent of the object. This distinction becomes very important with respect to dragging objects. An example of this distinction is given after the section “Dragging.”

A point constructed by itself is called a basic point.

An independent object is an object created using only basic points. Independent objects can be moved (dragged) but not modified directly. By moving the basic points used for their construction, you can modify them indirectly.

A dependent object is an object constructed using an independent object (or another dependent object). Dependent objects cannot be moved (dragged) or modified directly. You can move or modify them indirectly by moving the basic points or independent objects responsible for their existence.

The more elaborate a construction becomes, the more difficult it can be sometimes to distinguish these types. However, the Cabri Geometry II software will assist you.

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Dragging

Dragging objects is valuable for generating conjectures. You can modify an object by dragging all or part of it to a new location. Whether or not an object can be changed depends directly on how it was created.

You can drag (move) a basic point to a new location, modifying, in turn, any object constructed

Pointer

using it. An independent object can be modified with one of the tools from the cannot alter a dependent object directly by dragging, but you can change it by dragging the basic points used in its construction.

toolbox. You

Whenever an object can be dragged, the pointer changes to the then to the

dragging hand

% cursor. When the % is visible, the selected object follows the pointer as

selection hand

& momentarily and

you move it.

If your computer's performance is sluggish, you may need to move the pointer to the location you want and wait for the computations to finish with the new characteristics. This is particularly evident when there are many objects in the drawing window.

If the object is dependent (cannot be dragged), the pointer changes to the reverts to the

cross hair

! cursor.

selection hand

& and then

Example 3: Evaluating basic points, independent objects, and dependent objects

1. Construct the perpendicular bisector of a side of a triangle (see Example 2).

(The vertices are basic points, the triangle is an independent object, and the perpendicular bisector is a dependent object.)

2. Basic points:

Pointer

Select

from the

Pointer

toolbox.

Move the ! near a vertex of the triangle (the cursor changes to the $ with the message

Press and hold down the mouse button.

The cursor changes to the & and then almost immediately to the %.

When you drag the point, the triangle changes its size and shape, and the perpendicular bisector changes accordingly.

These results are characteristics of using a basic point.

An inquiry that could be made here is: “When does the

perpendicular bisector of one side of a triangle contain a vertex of the triangle?”

This point

Chapter 1: Learning the Basics 1-13

Constructing Objects

(Continued)

3. Independent objects:

Move the ! near a side of the triangle (the cursor changes to the $ with the message

Press and hold down the mouse button.

The cursor changes to the & and then almost immediately to the %.

Continue to hold down the mouse and move the triangle about the drawing window.

The triangle does not change its size or its shape, while the perpendicular bisector moves along with the triangle. The triangle was constructed using three basic points as its vertices; therefore, it is an independent object and can be moved.

4. Dependent objects:

Move the ! near the perpendicular bisector (the cursor changes to the $ with the message

Press and hold down the mouse button.

This triangle

This line

The cursor changes to the & and then almost immediately back to the !.

The perpendicular bisector cannot be modified directly; it is a dependent object.

Note: You can modify the perpendicular bisector indirectly by dragging the basic points or the independent objects used for its creation.

Example 4: Creating the circumcenter of a triangle

1. Construct the perpendicular bisector of one side of a triangle (see Example 2.)

2. Construct the perpendicular bisector of a second side.

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3. Choose

Intersection Point(s)

from the

Points

toolbox.

4. Point to one of the perpendicular bisectors (the cursor message

This line

appears) and click once.

The line changes to marquee outline.

5. Point to the other perpendicular bisector. After the cursor message appears, click once.

The first line returns to solid, and a point at the intersection of the two lines appears. This point of

This line

intersection is known as the circumcenter of the triangle.

The vertices of the triangle are basic points. The triangle is an independent object because its existence depends only upon basic points. The perpendicular bisectors are dependent objects because their existence depends upon independent objects (the sides of the triangle). The circumcenter is a dependent object because it was created using dependent objects (the perpendicular bisectors).

In Example 5, we will first create a circle, and then inscribe a triangle. You can move the circle by dragging its center point or modify it by dragging its circumference. The triangle cannot be moved. However, you can modify it by dragging any one of its vertices around the circle.

Example 5: Inscribing a triangle in a circle

1. Choose

Circle

from the

Curves

toolbox.

2. Move the # to any place in the drawing window and click once.

A flashing point appears.

3. Move the cursor away from the flashing point.

A circle appears with the flashing point as its center.

Click again to finish constructing the circle.

Note: The flashing point changes to solid to indicate the construction is completed.

Chapter 1: Learning the Basics 1-15

Constructing Objects

(Continued)

4. Choose

Triangle

from the

Lines

toolbox.

5. Move the # to any point of the circle (the cursor message

On this circle

appears), and click once.

6. Move the cursor to a second and third point on the circle, clicking once at each point.

A triangle becomes inscribed in the circle.

7. Choose

Pointer

from the

Pointer

toolbox.

8. Move the ! cursor near the center point (the cursor message

This point

appears).

Press and hold down the mouse button until the % appears, and drag the center point around the drawing window.

On this circle

Note: The radius of the circle remains unchanged.

9. Move the ! near the circumference of the circle (the cursor message

This circle

appears).

Press and hold down the mouse button until the % appears, and drag the circumference.

Note: The center point of the circle remains fixed while the radius changes, and the vertices of the triangle stay on the circle.

10. Move the ! near a vertex of the inscribed triangle (the cursor message

This point

appears).

Press and hold down the mouse button until the % appears, and then drag the point.

Note: The point can only be moved along the circle.

If you move the pointer while creating points, Cabri Geometry II reverts to dragging. This feature anticipates your intent to modify your construction without requiring you to return to the

Pointer

toolbox. However, it can create some confusion if you are creating points quickly and inadvertently move the pointer while pressing the mouse. In this case, a point will not be created.

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Using the Undo/Redo command

You can cancel an operation that has just been completed by using the

Edit

menu. Only the most recent operation can be undone.

To review additional steps in your construction, see the

Replay Construction

Undo/Redo

command in the

Edit

menu. This command allows you to replay each step of a construction.

Deleting objects

Delete objects by selecting them, and then pressing

Edit

menu.

DELETE

or selecting the

Select multiple objects by pressing the mouse in free space and dragging a marquee rectangle around the objects to be deleted. Only objects that are fully enclosed by the marquee rectangle will be deleted. All selected objects are displayed in marquee outline.

Select all objects in the drawing window by using the press

DELETE

pressing pressing

or select

COMMAND+A DELETE

Clear

from the

(Macintosh) or

Edit

menu. You can also clear the entire drawing window by

CTRL+A

(Windows, DOS) simultaneously, releasing, then

Select All

command in the

WARNING! When an object is deleted, all objects that depend on that object are deleted as well. It is possible to delete an entire construction by deleting a single point. If you accidentally delete an object, you can recover it by using the

Undo/Redo

command in the

Edit

menu.

Example 6a: Deleting objects — Method 1

Clear

command in the

Edit

menu. Then

1. Construct a circle and an inscribed triangle (see Example 5).

2. Select

Pointer

from the

Pointer

toolbox.

3. Point to the center point of the circle and click.

The center point flashes.

Press the

DELETE

key.

The point, the circle, and the triangle disappear.

This point

Chapter 1: Learning the Basics 1-17

Constructing Objects

(Continued)

Example 6b: Deleting objects — Method 2

1. Repeat steps 1 and 2 in Method 1, or select

Edit

the

menu.

Undo/Redo

2. Point to the circle and click.

The circle appears in marquee outline.

Press the

DELETE

key.

The circle and the triangle disappear, but the center point remains.

Example 6c: Deleting objects — Method 3

1. Repeat steps 1 and 2 in Method 1, or select

Undo/Redo

2. Point to the triangle and click.

Press the

DELETE

key.

The triangle disappears, but the circle, its center point, and the vertices of the triangle remain.

Example 6d: Deleting objects — Method 4

This circle

This triangle

1. Repeat steps 1 and 2 in Method 1, or select

Undo/Redo

2. Point to a vertex of the triangle and click.

Press the

DELETE

key.

What happened? How does this differ from Method 3?

This point

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Changing the Appearance of Objects

You can change the appearance of objects from the

Access the

Attributes

toolbox, use the

toolbar from the

Fill, Thick, Dotted

To apply attributes from tools in the modified. To use an option from the

Hide/Show Attributes

Modify Appearance

, or

Draw

menu, select the tool, and then select the object to be

Attributes

toolbar, first select the objects to be modified, and

Attributes

toolbar or the

command in the

tools.

Draw

Options

toolbox.

menu. In the

then select the attribute.

Labeling objects

You can label points in two ways — as you create them or with the

Label

tool in the

Labeling objects as they are created is intended for quick access and is limited to five alphanumeric characters. Editing is not available at this stage. However, after constructing the

Label

object, you can edit the label with the

tool.

Example 7a: Adding labels during construction

1. Select

Triangle

from the

2. Click on the drawing window. Then type

A point appears with a label

Lines

toolbox.

beside it.

Display

toolbox.

Draw

3. Move the # , click once, and then type

Another point, a segment connecting the two points,

and a label

4. Move the # to a new position, click once, and type

The completed triangle appears as well as the label

appear.

beside the last point created.

The

Label

tool in the

Display

toolbox allows you to attach labels to a point, line, or circle. Once

attached to the object, labels cannot be detached. You can position them near the object using the

Pointer

, and they will retain that position through all modifications to the object.

Chapter 1: Learning the Basics 1-19

Constructing Objects

(Continued)

Example 7b: Adding labels after construction

1. Select

Triangle

from the

Lines

toolbox.

2. Construct a triangle on the drawing window.

3. Select

Label

from the

Display

toolbox.

4. Move the ! near a vertex of the triangle.

The cursor changes to the I-beam I (the cursor message

This point

appears).

5. Click once and an edit box appears.

Note: (Macintosh only) On the top row are four options that generate pull-down menus:

for font size, F for font style, and the last box for text

for font character set,

color.

This point

6. Type a name for the vertex, and then click anywhere

New York City

outside the edit box.

The box disappears, but the name remains.

7. Repeat for the other vertices.

Los Angeles Miami

You can also apply comments to measurements immediately after creating them. Just begin typing characters after creating the measurement.

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Example 8: Comments

1. Select

Triangle

from the

2. Construct a triangle and label its vertices

3. Select

Area

from the

Lines

toolbox.

Measure

toolbox.

A, B

, and C.

4. Move the cursor to a side of the triangle until it changes to the $ (the cursor message

This triangle

appears), and

click once.

Depending on the triangle and the default settings, a

number and units label, such as 4.520 cm

5. Begin typing the comment

Area of ABC =

, appears.

The comment attaches to the left side of the measurement.

6. Select

Comments

from the

7. Move the 4 near the area (the cursor message

text

appears and the cursor changes to the I).

Display

toolbox.

Edit this

Click once and an edit box appears with the value of the area and the comment entered in step 5 on the text line.

This triangle

Area of ABC = 4.520 cm

8. Move the cursor between line, and add the word

The text now reads

“of”

triangle

Area of triangle ABC = 4.520 cm

“

9. Click on the toolbar or press

ESC

ABC

“

and

to make the edit box disappear, leaving the comment on the drawing window.

”

in the text

Area of ABC = 4.520 cm

.”

Area of triangle ABC = 4.520 cm

Chapter 1: Learning the Basics 1-21

Constructing Objects

(Continued)

Scrolling the drawing window

You can scroll the drawing window within a one-square-meter region by three methods:

4 Use the Show Drawing command in the File menu to view the entire one-square-meter region

in compressed form. You can reposition the active widow, which allows you to work in another section of the drawing. (Note: When you click and hold the mouse button, the grasping hand cursor ()) appears.)

4 Use the scroll bars on the right and bottom sides of the drawing window (Macintosh only).

Clicking on the scroll bars or buttons moves the drawing in a horizontal or vertical direction.

4 Press the

left mouse button. The screen scrolls in the direction that you move the pointer.

COMMAND

key (Macintosh) or the

key (Windows, DOS), then press down on the

CTRL

Saving and printing

You can save a construction to a file at any time using the menu. If the construction has never been saved, these two commands have the same effect.

Save

The stored. If the construction has already been saved, the has been modified since the previous save. The new version of the construction replaces the older one.

The the older version.

You can print your Cabri Geometry II constructions on a printer. Printed constructions enhance understanding by providing accurate, printed-to-scale manipulatives. The entire one-square-meter drawing or a specified portion can be printed in both black and white, or color.

dialog box allows you to name the construction and to choose the folder where it will be

Save as...

command allows you to save the figure to another folder or name without deleting

Save

command is active only if the figure

Save as...

and

commands in the

File

1-22 Chapter 1: Learning the Basics

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+ 106 hidden pages

Texas instruments CABRI GEOMETRY II Guidebook

Specifications and Main Features

Frequently Asked Questions

User Manual

Important

Permission to Print

TI Product and Services Information

About Cabri Geometry II

About the Developers

Cabri Geometry II Features

Table of Contents

About this Guidebook

Structure

Definitions

Chapter 1: Learning the Basics

First Steps

Checking system requirements

Installing Cabri Geometry II

Installing Cabri Geometry II on a network

Starting Cabri Geometry II

Optimizing your Macintosh system configuration

Changing your Macintosh system configuration using Cabri II

The Cabri Geometry II window

Elements of the Cabri Geometry II window

About menus and toolboxes

Accessing on-line help

Constructing Objects

Pointers that guide you

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