Texas Instruments Cabri Geometry II Manuel

CABRI GEOMETRYëII

Guidebook for Macintosh

, Windows

, and MS-DOS

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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 GEOMETRYII

Guidebook

for Macintoshë, Windowsë,

and MS-DOSë

Dive into Geometry

Copying permitted provided TI copyright notice is included

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.

iii

Copying permitted provided TI copyright notice is included

Table of Contents

About this Guidebook .................................................................. vi

CHAPTER 1: LEARNING THE BASICS ............................................. 1–1

First Steps............................................................................. 1–2

Constructing Objects ................................................................... 1–10

CHAPTER 2: USING THE MENUS................................................... 2–1

File Menu ............................................................................. 2–2

Edit Menu ............................................................................. 2–5

Options Menu.......................................................................... 2–7

Help Menu............................................................................. 2–12

CHAPTER 3: USING THE POINTER TOOLBOX.................................... 3–1

Pointer................................................................................ 3–2

Rotate ................................................................................ 3–3

Dilate ................................................................................. 3–4

Rotate and Dilate....................................................................... 3–5

CHAPTER 4: USING THE POINTS TOOLBOX...................................... 4–1

Point.................................................................................. 4–2

Point on Object ........................................................................ 4–3

Intersection Point(s) ................................................................... 4–4

CHAPTER 5: USING THE LINES TOOLBOX........................................ 5–1

Line .................................................................................. 5–2

Segment............................................................................... 5–4

Ray ................................................................................... 5–5

Vector ................................................................................ 5–6

Triangle ............................................................................... 5–7

Polygon ............................................................................... 5–8

Regular Polygon ....................................................................... 5–9

CHAPTER 6: USING THE CURVES TOOLBOX..................................... 6–1

Circle ................................................................................. 6–2

Arc ................................................................................... 6–3

Conic ................................................................................. 6–4

Copying permitted provided TI copyright notice is included

CHAPTER 7: USING THE CONSTRUCT TOOLBOX ............................... 7–1

Perpendicular Line ..................................................................... 7–2

Parallel Line ........................................................................... 7–3

Midpoint .............................................................................. 7–4

Perpendicular Bisector.................................................................. 7–5

Angle Bisector ......................................................................... 7–6

Vector Sum ............................................................................ 7–7

Compass .............................................................................. 7–8

Measurement Transfer .................................................................. 7–9

Locus ................................................................................. 7–11

Redefine Point ......................................................................... 7–13

Redefine Object ........................................................................ 7–14

CHAPTER 8: USING THE TRANSFORM TOOLBOX............................... 8–1

Reflection ............................................................................. 8–2

Symmetry ............................................................................. 8–3

Translation ............................................................................ 8–4

Rotation............................................................................... 8–5

Dilation ............................................................................... 8–6

Inverse................................................................................ 8–7

CHAPTER 9: USING THE MACRO TOOLBOX ..................................... 9–1

How to create a macro .................................................................. 9–2

Initial Object........................................................................... 9–3

Final Object ........................................................................... 9–4

Define Macro .......................................................................... 9–5

CHAPTER 10: USING THE CHECK PROPERTY TOOLBOX ...................... 10–1

Collinear .............................................................................. 10–2

Parallel ............................................................................... 10–3

Perpendicular.......................................................................... 10–4

Equidistant ............................................................................ 10–5

Member ............................................................................... 10–6

Copying permitted provided TI copyright notice is included

Table of Contents (continued)

CHAPTER 11: USING THE MEASURE TOOLBOX ................................. 11–1

Distance & Length...................................................................... 11–2

Area .................................................................................. 11–3

Slope ................................................................................. 11–4

Angle ................................................................................. 11–5

Equation & Coordinates................................................................. 11–6

Calculate .............................................................................. 11–7

Tabulate .............................................................................. 11–11

CHAPTER 12: USING THE DISPLAY TOOLBOX................................... 12–1

Label ................................................................................. 12–2

Comments............................................................................. 12–3

Numerical Edit......................................................................... 12–5

Mark Angle ............................................................................ 12–7

Fix/Free............................................................................... 12–8

Trace On/Off........................................................................... 12–9

Animation ............................................................................. 12–10

Multiple Animation ..................................................................... 12–11

CHAPTER 13: USING THE DRAW TOOLBOX...................................... 13–1

Hide/Show ............................................................................ 13–2

Color ................................................................................. 13–3

Fill ................................................................................... 13–4

Thick ................................................................................. 13–5

Dotted ................................................................................ 13–6

Modify Appearance..................................................................... 13–7

Show/Hide Axes ....................................................................... 13–8

New Axes ............................................................................. 13–9

Define Grid ..................................................................................................... 13–10

INDEX............................................................................. INDEX–1

Copying permitted provided TI copyright notice is included

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 Windowséand 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 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.

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

top of the object you wish to select.

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

pointing to a specific location

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

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

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.

Chapter 1: Learning the Basics 1-1

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

1-2 Chapter 1: Learning the Basics

Copying permitted provided TI copyright notice is included

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.

¦ 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.

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.

¦ 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

Cabri II

on your hard

disk.

2. Insert the Cabri Geometry II Macintosh

diskette in your floppy disk drive.

3. Double-click on the

Installer

on the diskette

and follow the directions on the screen.

1. Insert the Cabri Geometry II DOS diskette

in your floppy disk drive.

2. At the DOS prompt, enter:

A:\INSTALL or B:\INSTALL, and then

follow the screen prompts.

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

RUN

and

enter A:\SETUP, and then follow the screen

prompts.

1. Insert the Cabri Geometry II for Windows

diskette #1 in your floppy disk drive.

2. Click on

START/RUN

and enter A:\SETUP,

and then follow the screen prompts.

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.

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