Texas instruments TI-92 PLUS, TI-89 Cabri Geometry

TI-89 / TI-92 Plus / Voyage™ 200 Cabri Geometry

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Cabri Geometry Application User Guide

Preview of Geometry................................................................................. 2

Learning the Basics.................................................................................... 3

Managing File Operations ....................................................................... 12

Managing File Operations (Continued)................................................. 13

Setting Application Preferences ............................................................ 14

Selecting and Moving Objects ................................................................ 17

Deleting Objects from a Construction .................................................. 18

Creating Points......................................................................................... 19

Creating Lines, Segments, Rays, and Vectors ...................................... 21

Creating Circles and Arcs ....................................................................... 24

Creating Triangles.................................................................................... 26

Creating Polygons .................................................................................... 27

Constructing Perpendicular and Parallel Lines ................................... 29

Constructing Perpendicular and Angle Bisectors ............................... 31

Creating Midpoints .................................................................................. 32

Transferring Measurements ................................................................... 33

Creating a Locus....................................................................................... 35

Redefining Object Definitions ................................................................ 36

Translating Objects.................................................................................. 37

Rotating and Dilating Objects ................................................................ 38

Creating Reflections and Inverse Objects ............................................ 43

Measuring Objects ................................................................................... 46

Determining Equations and Coordinates.............................................. 48

Performing Calculations ......................................................................... 49

Collecting Data......................................................................................... 50

Checking Properties of Objects ............................................................. 51

Putting Objects in Motion ....................................................................... 55

Controlling How Objects Are Displayed............................................... 57

Adding Descriptive Information to Objects.......................................... 60

Creating Macros ....................................................................................... 63

Geometry Toolbar Menu Items .............................................................. 66

Pointing Indicators and Terms Used in Cabri Geometry.................... 68

Helpful Shortcuts ..................................................................................... 69

Index.......................................................................................................... 71

This document describes the Cabri Geometry application for the TI-89 / TI-92 Plus / Voyage™ 200 PLT. It provides descriptions, procedures, illustrations, and examples for using the TI-89 / TI-92 Plus / Voyage 200 PLT to perform analytic, transformational, and Euclidean geometric functions .

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 1

Preview of Geometry

Create a circle and construct a perpendicular line that is tangent to the circle.

Steps

1. Start a new geometry session.

In this example, G2 is the name of the

variable. You can use up to eight characters to name constructions (variables).

2. Create a circle.

Pressing

the center point. Pressing second time draws the circle.

the first time defines

the

3. Construct a segment from the center of the circle and attach it to the circumference.

TI-89

Keystrokes

DGj ¸

…1¸

B (hold momentarily to expand the

“THIS

)

A (until

“ON

circle)

„

A (until

you see

POINT”

you see

THIS CIRCLE”

TI-92 Plus /

Voyage™ 200

PLT Keystrokes

¸D

¸¸

…1¸ B

(hold momentarily to expand the

circle)

„5A

you see

POINT”

you see

)

THIS CIRCLE”

(until

“THIS

)

“ON

(until

Display

)

4. Construct a line perpendicular to the segment at the intersection point of the segment and the circle.

Observe each displayed message

before pressing

The resultant perpendicular line is

tangent to the circle.

5. Observe what happens when the endpoint of the segment is dragged around the circle.

†1¸ ¸

Press and hold

j then press C

†1¸ ¸

Press and hold

‚

then press

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 2

Learning the Basics

This section describes the basic operations that you need to know, such as selecting items from the various menus, navigating with the cursor pad, and starting a construction.

Starting Geometry

Important:

requires 25 Kbytes minimum of free memory

Note:

can be up to eight characters.

Cabri Geometry

The variable name

To start a new geometry session:

Press ´.

Press

3. Type a variable name in the twice. The Cabri Geometry application window opens as shown below.

and select

Cabri

, then

dialog box and press

New

3:New

Selecting a Tool/Command

You construct objects in the active drawing window. The

TI-89

drawing window is 158 pixels horizontally and 76 pixels vertically. The

TI-92 Plus /

Voyage 200 PLT drawing window is 239 pixels

horizontally and 103 pixels vertically.

The toolbar is comprised of eight separate menus that are selected when you press the function keys. Each menu in the toolbar contains an icon that graphically illustrates a geometry tool or command. The active menu is framed as shown by the first menu item in the previous figure. The table on the next page lists the menu function keys

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 3

Learning the Basics

On the TI-89, press:

„

…

†

‡

2ˆ

2‰

(continued)

On the TI-92 Plus / Voyage™ 200 PLT press:

to perform freehand

transformations.

to construct points or linear

„

objects.

to construct curves and

…

polygons.

to build Euclidean

†

constructions and create macros.

to build transformational

‡

geometry constructions.

to perform measurements and

calculations.

to annotate constructions or

‰

animate objects.

Moving the Cursor

2Š

to perform file operations and

edit functions.

To select tools or commands in a menu, press the number that corresponds to the menu item or use the cursor pad to move up and down through the menu and press

to select the highlighted

menu item.

For most menu items, once a menu item is selected, it remains in effect until another menu item is selected. The exceptions default to the

Pointer

toolbar menu and all

tool; they are the

toolbar menu items.

File

Define Macro

tool in the

Construct

To move the current active cursor in one of eight directions, press the cursor pad: up, down, left, right, and the four corresponding diagonals on the

TI-92 Plus

. On the

/ Voyage 200 PLT, hold down

TI-89

any two adjacent cursor keys to move diagonally. The cursor moves one pixel for each keypress. When used in combination with the

TI.89:

TI.92 Plus / Voyage 200 PLT:

key, the cursor moves

‚

one pixel for each keypress and five pixels in repeat mode (cursor pad is held down).

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 4

Learning the Basics

Placing Points

All objects are constructed using one or more points. You create or select points when a tool is active. The order of operation is:

To create a point, select the create points anywhere in the plane when the construction pencil (#) is active. For example, to construct the two points in the plane below:

(continued)

Select a construction tool.

Create or select the required points that define the object.

Press „ and select

1:Point

tool and press

Point

. You can

Move the (#) cursor to the desired location and press

to create the first point.

To create the second point, press the right side of the cursor pad (B) until the

first point second point

cursor is at the desired location then press

Creating a Simple Triangle

All other objects require multiple points to complete their construction. For example, to construct a triangle, you create three points as shown below:

Press … and select

Move the (#) cursor to the desired

location and press

3:Triangle

to define

third point

the first point.

Move the cursor to another location,

and press

to define the second

point.

Move the cursor to the third location

and press

again to complete

first point second point

the triangle.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 5

Learning the Basics

Selecting Objects

when

to select

Press

Hint:

pressing multiple objects.

To select objects, point to the object and press marquee (dotted) rectangle around the objects. To deselect selected objects, move the cursor to an unoccupied location in the plane and press

Selecting one object.

The selected object appears as a

Method #1: Selecting multiple objects.

All selected objects appear as a

(continued)

Move the cursor using the

Pointer

tool until the object’s name appears and press

marquee outline.

Move the cursor using the

Pointer

tool until the object’s name appears, then hold ¤ and press

Repeat step 1 for other objects that you want to select (the circle and triangle in this example).

marquee outline.

or draw a

Select an object.

Select the objects.

The Pointer must

Note:

begin in an unoccupied location in the plane.

Method #2: Selecting multiple objects.

Press and hold

TI-89:

‚

›

TI-92 Plus / Voyage™ 200 PLT:

‚ and press the cursor pad to draw a marquee rectangle around the objects that you want to select.

Release

TI-89: TI-92 Plus / Voyage 200 PLT:

‚ (The circle, triangle, and their points are selected in this example.)

All selected objects appear as a

marquee outline.

Draw a marquee rectangle around the objects.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 6

Learning the Basics

Deleting Objects

Labeling Points and Objects

A point appears with

Note:

a label “a” beside it.

Another point, a

Note:

segment connecting the two points, and a label “b” appear.

: The completed

Note

triangle appears as well as the label “c” beside the last point created.

To delete objects, select them using the procedures described on the previous page and press 0 (backspace key) or

TI-92 Plus / Voyage™ 200 PLT:

in the

You can label points and objects in the following two ways:

Labeling objects as they are created is intended for quick access and is limited to five alphanumeric characters. Label editing is not available; however, after constructing the object, you can edit a label with the

(continued)

Š then select

toolbar menu).

File

As you create them (see below).

With the

Label

Press … and select

Label

tool.

tool in the

3:Triangle

Display

menu (see page 60).

Move the (#) cursor to the desired location and press

to create the

first point. Press

TI.89: TI-92 Plus / Voyage 200 PLT:

Move the cursor and press

create the second point then press

TI.89: TI-92 Plus / Voyage 200 PLT:

Move the cursor and press

create the third point then press

TI.89: TI-92 Plus / Voyage 200 PLT:

2Š

TI-89:

7:Delete

Define and label the first point.

Define and label the second point.

Define and label the third point.

(delete option

Dependent and Independent Objects

You create all objects using one or more points. The manner in which you create an object determines whether or not it is dependent or independent of the object. This distinction becomes important with respect to dragging objects.

A point constructed by itself is called a points, select the

Voyage 200 PLT:

Pointer

‚ once. All basic points will flash and can be

tool and press

basic point

TI-89:

. To identify basic

TI-92 Plus /

dragged.

independent object

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

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 7

Learning the Basics

dependent object

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.

Dragging Objects

To lock the cursor

Hint:

in drag mode, press:

[

a-lock

]

2 ‚

TI-89: TI-92 Plus / Voyage™ 200 PLT:

You can move constructed objects that you define with the tool anywhere in the plane. For example, to reposition a constructed object:

The message “

(continued)

is an object constructed using an independent

Construct a triangle as previously described on page 5.

Press ƒ and select

1:Pointer

Position the (+) cursor until it changes to the (å) cursor.

THIS TRIANGLE”

appears.

Press and hold

TI-89: TI-92 Plus / Voyage 200 PLT:

‚

to use the dragging hand then press and hold B to move the triangle to the right.

Pointer

Positioning a Construction

Multi-Step Constructions

To scroll the drawing window to anywhere within the virtual working area (see page 58), press 2 and the cursor pad at the same time. The default position of the active drawing window is at the center of the virtual working area.

Construct several geometric

objects as shown.

Press ƒ and select

Press and hold 2 then press

1:Pointer

the cursor pad to scroll all objects in the active drawing window.

open hand scroll cursor

You perform multi-step constructions by repeating the construction of individual points described in this section. Lines require one point and a direction, line segments require two points, triangles and arcs require three points, and polygons require n points where n is greater than two.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 8

Learning the Basics

To illustrate the basic steps in this section, the following procedure will construct and measure a circle circumscribed around a triangle.

(continued)

Press

TI-89: TI-92 Plus / Voyage™ 200 PLT:

select

2Š

3:New

Š and

Type a name for the variable to start a new construction and press

twice.

Construct and label a triangle. (Perform steps 1 through 4 in “Labeling Points and Objects” described on page 7.)

Construct perpendicular bisectors for two sides of the triangle by pressing

and selecting

†

Bisector

4:Perpendicular

Select side

and press

Start a new construction.

Construct and label a triangle.

Construct the first perpendicular bisector.

Select side

Modify the appearance of the

and press

perpendicular bisectors from solid to dotted lines by pressing

TI-89: TI-92 Plus / Voyage 200 PLT:

select

Select a line and press

2‰

9:Dotted

‰ and

Complete the perpendicular bisectors.

Modify the lines.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 9

Learning the Basics

10.

11.

12.

Press the cursor pad (B and D) until

(continued)

Repeat step 8 for the other perpendicular bisector.

Press … and select

1:Circle

Define the center point of the circle by moving the cursor near the intersection of the perpendicular bisectors until the message “

THIS INTERSECTION

press

” appears and

POINT AT

To complete construction of the circle, press the cursor pad B to expand the circle.

the cursor is near one vertex of the triangle and the message “

RADIUS POINT

to complete the circle.

” appears, then press

THIS

Define the center point.

Complete the circle.

Measure the circumference of the

13.

circle by pressing

TI-89: TI-92 Plus / Voyage™ 200 PLT:

selecting

Position the cursor near the circle

14.

until the message “

OF THIS CIRCLE

2ˆ

1:Distance & Length

CIRCUMFERENCE

” appears and press

Measure the circumference.

ˆ and

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 10

Learning the Basics

Using Undo

Press

Hint:

To undo the last fully constructed object or operation, press

TI-89: TI-92 Plus / Voyage™ 200 PLT:

and select

(continued)

2Š

D:Undo

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 11

Managing File Operations

File

The that let you open, close, and save geometry constructions.

toolbar menu contains file-management commands

Opening a Construction or Macro

Pressing

Note:

selecting selecting the command lets you open and use a previously saved macro.

2:Macro

Open

and after

Saving a Construction as Another Name

The

command opens a dialog box for opening an existing

Open

geometry figure or macro.

Press

TI-89: TI-92 Plus / Voyage™ 200 PLT:

and select

Select the type of variable that you

want to open,

Press the cursor pad to highlight the

variable name that you want to open and press

2Š

1:Open.

Figure

twice.

Macro

To preserve memory, the TI-89 / TI-92 Plus / Voyage 200 PLT uses an “edit-in-place” method while you are constructing objects. This means the variable that you named when you first opened the geometry session is constantly updated during your constructions.

The

Save Copy As

command opens a dialog box that lets you save

the current construction to a variable name that you specify.

Press

TI-89: TI-92 Plus / Voyage 200 PLT:

and select

Enter a name for your construction

in the

2Š

2:Save Copy As

Variable

box and press

twice.

Starting a New Construction

The for creating a construction or macro.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 12

command opens a new, blank Geometry drawing window

New

Press

TI-89: TI-92 Plus / Voyage 200 PLT:

and select

2Š

3:New

Managing File Operations (Continued)

Press D and enter a name, up to

eight characters, for your new construction and press twice.

A blank construction area appears.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 13

Setting Application Preferences

Geometry Format Dialog Box Options

Defining Application Preferences

The

File

toolbar menu contains the

Format

command that opens a dialog box to specify application preferences, such as angles in degrees or radians and the display precision of calculations.

The

Format

command opens the

Geometry Format

dialog where you specify application preferences. The default formats are shown below.

The contents of the

Geometry Format

dialog box are included in your saved construction files. Consequently, when you open a saved construction, the application returns to the same configuration that was used when you developed the construction.

Press

TI-89: TI-92 Plus / Voyage™ 200 PLT:

and select

2Š

9:Format

To display all options, press D until the cursor is on the same

line as the item that you want to change and press B.

Select the desired option. (Press the appropriate digit or highlight

the option and press

To save your changes and close the dialog box, press

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 14

Setting Application Preferences

(continued)

Format Options and Descriptions

Option Description

Coordinate Axes

1:OFF 2:RECTANGULAR 3:POLAR 4:DEFAULT

The following table describes each option in the dialog box. (Default settings are in boldface.)

Displays the rectangular or polar axes.

The default distance for the tick marks is approximately 5 mm each. To change this scale, select any tick mark on the horizontal axis and drag it to a location that approximates the desired scale. All the tick marks in the horizontal and vertical axes will change accordingly.

To change the scale for only the y axis, drag any tick mark on the vertical axis. The scale of constructed objects is not affected when you change the coordinate scale.

To rotate the axes 360 degrees to redefine the major axes, drag the x axis in a circular direction. You can also rotate the y axis independently to create an oblique coordinate system. Constructed objects do not change.

Grid

1:OFF 2:ON

Displays a grid that is composed of a dot at each coordinate. The example below shows the rectangular coordinate axes with grid marks turned

. The grid does not represent a polar

coordinate system.

Geometry Format

# of Locus Points

5 10 15

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 15

Determines how many objects will be constructed along the designated path when you construct a locus.

The complete option list is: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80, 90, 99.

To modify this value dynamically in your construction, select the locus and press « to increase the number of locus points or

to decrease the number of locus points.

Setting Application Preferences

(continued)

Option Description

Link Locus Points

1:OFF

2:On

Envelope of Lines

1:OFF

2:On

Display Precision

1:FIX 1

2:FIX 2

C:FIX 12

Length & Area

1:PIXELS 2:MM

3:CM

4:M

Angle

1:Degree

2:RADIAN

When this option is of linear interpolation. When this option is are displayed.

When this option is displayed when you construct the locus of a line. When this option is

Determines the display precision for calculations and

, each line of the locus is displayed.

OFF

measurements in your constructions.

To modify this value dynamically in a construction, select the number and press « or | to increase or decrease the displayed precision of that number.

Determines the default units for measurements in your constructions. All values are converted to the selected unit.

Determines the angle units that are displayed and the geometry calculator mode. All angles are converted to the selected unit.

This in the

preference is independent from the

Angle

dialog box, which applies to other applications.

Mode

, the points of a locus are linked by way

, only the envelope of the line is

, only the points

OFF

preference

Angle

Line Equations

1:y=ax+b

2:ax+by+c=0

Circle Equations

1:(x.a)2+(y.b)2=r2

2:x

2+y2

+ax+by+c=0

Determines the format for displayed line equations.

Determines the format for displayed circle equations.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 16

Selecting and Moving Objects

Pointer

The geometry pointer features. These features let you select objects and perform freehand transformations.

toolbar menu contains the tools associated with

Selecting and Moving Objects Using the Pointer Tool

To select multiple

Tip:

objects, press selecting an object.

while

The

Pointer

tool lets you select, move, or modify objects. Pressing the cursor pad lets you move the The primary functions of the

Pointer

scrolling.

To return to the

To see how the

Construct a triangle as previously

Pointer

at any time, press N.

tool works:

described.

Press ƒ and select

3. Selecting:

to it and press

To select an object, point

1:Pointer

when the cursor

message appears for that object.

To deselect an object, point to an unoccupied location and press

Pointer

in one of eight directions.

are selection, dragging, and

Point to the object.

Select the object.

: Sometimes multiple

ote

objects cannot be moved concurrently. Dependent objects cannot be moved directly. If a selected object cannot be moved directly, the cursor reverts to the cross hair of dragging hand cursor.

cursor instead

(+)

4. Moving:

To move an object, drag it to a new location. (Only the last object is actually displayed.)

To show all the points that can be

moved, position the cursor to an unoccupied location and press

TI-89: TI-92 Plus / Voyage™ 200 PLT:

‚

Drag the object.

once. The points that you can drag will flash.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 17

Deleting Objects from a Construction

File

The selected objects or all objects from a construction.

toolbar menu contains commands that let you delete

Delete Defined Objects

Use Undo

Hint:

recover an inadvertent deletion.

( ¥ Z)

Deleting All Objects

The

Select the object that you want to

command lets you delete selected objects.

Delete

delete. (To select additional objects, press ¤ while selecting each item.)

In this example, only the triangle

Note:

and not the points of the vertices are selected.

Press

TI-89: TI-92 Plus / Voyage™ 200 PLT:

and select

2Š

7:Delete

to delete the

selected objects.

The

Clear All

command deletes every item in the construction and

clears the screen.

Press

TI-89: TI-92 Plus / Voyage 200 PLT:

and select

2Š

8:Clear All

A dialog box displays for you to

confirm this command.

Select the object.

Delete the selected object.

Press

to clear the entire

construction area or press N to cancel.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 18

Creating Points

Points and Lines

The

toolbar menu contains tools for creating and constructing points in geometry. The three point tools let you create points anywhere in the plane, on objects, or at the intersection of two objects.

Creating Points in Free Space and on Objects

The

tool creates points that can be placed anywhere in the

Point

plane, on existing objects, or at the intersection of any two objects.

If the point created is on an object, it will remain on the object

throughout any changes made to the point or to the object.

If the point is at the intersection of two objects, the point will

remain at the intersection when changes are made to the object or objects.

If the objects are changed such that they no longer intersect, the

intersection point disappears. The intersection point reappears when the objects again intersect.

To create points:

Press „ and select

2. Creating points in free space:

1:Point

Create points in free space.

Move the cursor to any location in the plane where you want a point and press

Creating points on objects:

to create the point.

Create points on objects.

Move the cursor to the location on an object where you want a point. When the cursor message appears, press

to create the point.

before after

You can attach a

Note:

label to the point by entering text (five-character maximum) from the keyboard immediately after creating a point.

Creating points with labels:

Create a point as defined in step 2 or 3 then press an appropriate alphabetic character key to create a label for the point.

Create points with labels.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 19

Creating Points

Creating a Point on an Object

Creating an Intersection Point

(continued)

The

Point on Object

tool creates points on any existing object. The point is placed at the location of the cursor. It remains permanently attached to the object—you can drag the point to move it, but it will always remain on the object.

Create any object, such as the

triangle shown in this example.

Press „ and select

Move the cursor toward the object

2:Point on Object

Point to the object.

until a cursor message appears for the object.

Press

to create the point.

Create the point.

The

Intersection Point

tool creates a point at the intersection (or intersections) of any two defined objects. If the objects are changed so that they no longer intersect, the intersection point disappears. The intersection point reappears when the objects again intersect.

Create any two intersecting objects,

such as the circle and line shown in this example. (If necessary, see pages 21 and 24.)

Press „ and select

Point

Select the first object of two

3:Intersection

intersecting objects then press

Select the second object then press

to create the intersection point

or points.

Select the first object.

Select the second object.

Points are created at each intersection.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 20

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