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Chapter 6: Using the Curves Toolbox 6-1

Copying permitted provided TI copyright notice is included
© 1997, 1999 Texas Instruments Incorporated

Chapter 6: Using the Curves Toolbox

The

Curves

toolbox contains the tools associated with curve features in Cabri Geometry II. These

features allow you to create curved objects, including ellipses, parabolas, and hyperbolas.

The illustration below shows the location of the

Curves

toolbox on the Cabri Geometry II toolbar,

along with its pull-down menu. Procedures for using tools in the

Curves

toolbox, including

examples, are presented in this chapter in the order in which the tools appear on the pull-down
menu.

Circle

Arc

Conic

Curves toolbox

Summary of Contents for Cabri Geometry II

Page 1: ...C A B R I G E O M E T R Y ë I I Guidebook for Macintoshë Windowsë and MS DOSë ...

Page 2: ...ses workshops or seminars with the accompanying Cabri Geometry II software provided each copy made shows the copyright notice Such copies may not be sold and further distribution is expressly prohibited Except as authorized above prior written permission must be obtained from Texas Instruments Incorporated to reproduce or transmit this work or portions thereof in any other form or by any other ele...

Page 3: ...C A B R I G E O M E T R Y I I Guidebook for Macintoshë Windowsë and MS DOSë Dive into Geometry ...

Page 4: ...sité 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 ...

Page 5: ...US 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 ...

Page 6: ... 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 Par...

Page 7: ...1 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 Gr...

Page 8: ... 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...

Page 9: ...ebook 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 toolb...

Page 10: ... 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 ...

Page 11: ...etup 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 t...

Page 12: ...w appears decrease the application memory size to a value that is compatible with your computer 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 Macintos...

Page 13: ... 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 currently available on your computer Check the Status field to determine if these values are acceptable Click on OK to continue Objects The amount of memory available is directly related to the number of objects that can be constructed Click on this button to optim...

Page 14: ...lustration Note The screen shown below illustrates the Macintosh version Screens on Windows and DOS systems are similar but slightly different Elements of the Cabri Geometry II window Drawing Window This region is where you build geometric constructions Menu bar The menu bar contains common graphic user interface menus for file management and editing together with Cabri Geometry II options Attribu...

Page 15: ...elp messages for each command Clicking on the A again removes the help window Help menu option Windows DOS Clicking on the Help menu option and selecting Help or pressing the F1 key toggles the help window ON and OFF Selection pointer 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 loca...

Page 16: ...aving or printing constructions Edit Commands for selecting or copying objects refreshing the drawing window or replaying constructions Options Commands for tool configurations hide show attributes preferences or setting software defaults Macintosh only Window Windows Standard Windows display options Help Windows DOS Help options TOOLBOXES Tools for Pointer Selecting or for free hand transformatio...

Page 17: ...when you click in the help window 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 b...

Page 18: ...ping hand The window can be scrolled using the mouse magnifying glass An ambiguity exists I beam I Text or numbers can be entered or edited paint brush 2 Color or attributes can be changed paint bucket 1 An object can be filled with a pattern or color crossed lines 4 The Comment option is active column width 3 The column width of the table can be adjusted Creating and selecting point s All objects...

Page 19: ...te 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 lo...

Page 20: ...an move drag it to a new location if it is an independent object and the Pointer 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 o...

Page 21: ...nter 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 selection hand and then reverts to the cross hair cursor Example 3 Evaluating basic points independent objects and dependent objects 1 Construct the p...

Page 22: ...e 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 This line Press and hold down the mouse button The cursor changes to the and then almost immediately back to the The perpendicular bisector cannot be modified d...

Page 23: ...cular 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 circumferen...

Page 24: ...d 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 ho...

Page 25: ...losed 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 Select All command in the Edit menu Then press DELETE or select Clear from the Edit menu You can also clear the entire drawing window by pressing COMMAND A Macintosh or CTRL A Windows DOS simultaneously releasing then pressing DELETE WARNING Whe...

Page 26: ...TE 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 1 Repeat steps 1 and 2 in Method 1 or select U...

Page 27: ...e Display toolbox 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 object you can edit the label with the Label tool Example 7a Adding labels during construction 1 Select Triangle from the Lines toolbox 2 Click on the drawing window Then type A A point appears with ...

Page 28: ...nges 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 C for font character set S for font size F for font style and the last box for text color 6 Type a name for the vertex and then click anywhere outside the edit box The box disappears but the name remains 7 Repeat for the o...

Page 29: ... 4 520 cm2 appears 5 Begin typing the comment Area of ABC The comment attaches to the left side of the measurement 6 Select Comments from the Display toolbox 7 Move the 4 near the area the cursor message Edit this text appears and the cursor changes to the I Click once and an edit box appears with the value of the area and the comment entered in step 5 on the text line 8 Move the cursor between of...

Page 30: ...ey Windows DOS then press down on the left mouse button The screen scrolls in the direction that you move the pointer Saving and printing You can save a construction to a file at any time using the Save and Save as commands in the File menu If the construction has never been saved these two commands have the same effect The Save dialog box allows you to name the construction and to choose the fold...

Page 31: ...ing menu options are available Each option is discussed in this chapter in detail according to its order on the pull down menus FILE MENU EDIT MENU OPTIONS MENU HELP New Open Close1 Save Save as Revert 4 Show Drawing 4 Show Page 3 Page Setup 5 Printer Setup 2 Print Quit Undo Redo Cut Copy Paste Clear Select all Select all Replay Construction Refresh Drawing Show Hide Attributes Defaults 1 Preferen...

Page 32: ...d to create the construction interactively by selecting Replay Construction in the Edit menu A macro appears in the Macro toolbox and may be used immediately in the construction A tool configuration file immediately alters the Cabri Geometry II tool configuration as defined in the file See Tool Configuration in the Options menu for more information A preference file immediately alters Cabri Geomet...

Page 33: ...is stage but you can position the window anywhere within the one square meter limits of the construction Drag the window to move it to a new section of your construction Click OK or Cancel to accept or cancel the operation 4 For the Macintosh the visible part of your construction can also be moved by clicking on the scroll bars or by dragging the drawing window while pressing the COMMAND key Press...

Page 34: ...elect a printer and respective print quality and to specify the page size US Letter US Legal or A4 Letter and orientation portrait or landscape Click on the selections to see the menu options The Printer option lets you select one of the printers listed below If your specific printer is not in this list select a printer that may be similar Note The print quality setting that you select may affect ...

Page 35: ...es two files CLIPCAB BMP and CLIPCAB FIG Copying a table that contains data creates the file CLIPCAB TXT Therefore to copy and paste a construction or table into another application such as a word processor or spreadsheet when using the DOS version select the objects and click on Copy Then open the other application and insert the appropriate BMP FIG or TXT file to the desired location Paste copie...

Page 36: ... version replays each step of a construction when you press the left and right arrow keys on the keyboard Pressing the right arrow key replays the construction in the forward direction and pressing the left arrow key replays the construction in the reverse direction Unlike the Macintosh and Windows versions you cannot edit a construction if you stop the replay before you reach the end of the const...

Page 37: ...ecify particular aspects of the program related to loci the coordinate system measurements and equation formats A dialog box as shown on the next page appears when you select this command The options are described below the illustration The settings specified in Preferences for the Macintosh and Windows versions can be saved to a Cabri Geometry II preferences file This file also contains the defau...

Page 38: ...ts adjacent points with a solid line Selecting the Envelope option draws only the envelope of a line as the locus rather than the locus of the line Coordinate System The default coordinate system can be set up for Cartesian or polar coordinates Displayed Precision Select the precision of the units displayed Cabri Geometry II always uses the maximum precision of the Macintosh when measuring objects...

Page 39: ...s You can rearrange or remove any tool in the toolbar You can place a tool configuration file in the preferences folder to automatically open Cabri Geometry II with the tool configuration specified in that file The following steps show you how to customize your toolbar 1 Select Tool Configuration in the Options menu 2 To remove any tool from its current toolbox select the tool The tool becomes att...

Page 40: ...d the next time you start Cabri Geometry II 4 Macintosh only Choose to attach a language to the Cabri Geometry II software Cabri Geometry II can recognize any language module that is in the same folder This command integrates the language as part of the Cabri Geometry II software 4 Macintosh only Choose to exclude a language from the Cabri Geometry II software If the And save in a file option is s...

Page 41: ...The point sizes in outlined text are sizes that your Macintosh should display without distortion The symbol is shown next to the default size The default size applies to labels comments numerical values and properties You can specify size independently for the Label Comments or Numerical Edit tools by first selecting the tool and then changing the size in this menu Point to another size to select ...

Page 42: ...ion about each toolbar icon and information about the Cabri Geometry II software Help Keyboard shortcut F1 DOS The Help command displays a description of the selected toolbar icon in the Help window at the bottom of the Cabri Geometry II screen For the Macintosh version click on A to open the Help window About Cabri II The About Cabri II command displays information about Cabri Geometry II that in...

Page 43: ...eometry II pointer features These features allow you to select objects and to perform freehand transformations The illustration below shows the location of the Pointer toolbox on the Cabri Geometry II toolbar along with its pull down menu Procedures for using Pointer tools including examples are presented in this chapter in the order in which the tools appear on the pull down menu Pointer Rotate D...

Page 44: ...ct by pointing and clicking when the cursor message appears for that object Select multiple objects by pressing the SHIFT key when selecting objects or by enclosing them in a marquee rectangle as shown in the example below Deselect an object by pointing to an unoccupied location and clicking Moving Move an object by dragging it to a new location Note Sometimes multiple objects cannot be moved conc...

Page 45: ...int and drag it in a circular motion Note Pressing the SHIFT key while dragging rotates the object in 15 degree increments Rotating about a defined point Select a desired rotation point and drag the object around the point Deselect the rotation point by clicking once in free space Note You can rotate an object automatically by using the Animation tool when the Rotate tool is visible on the toolbar...

Page 46: ...n object not a point and drag it away from its center to expand or toward its center to contract Note Dragging an object through its center causes a negative dilation Dilating about a defined point Select a desired dilation point and drag the object not the point in a linear motion Note You can dilate an object automatically by using the Animation tool when the Dilate tool is visible on the toolba...

Page 47: ...ate and Dilate Select Rotate and Dilate from the Pointer toolbox Note You can rotate and dilate an object automatically by using the Animation tool when the Rotate and Dilate tool is visible on the toolbar See the chapter Using the Display Toolbox for more information about Animation Examples Freehand rotation and dilation of an object about its geometric center Drag object in a circular or linear...

Page 48: ... Geometry II These features allow you to create points anywhere in the plane on objects or at the intersection of two objects The illustration below shows the location of the Points toolbox on the Cabri Geometry II toolbar along with its pull down menu Procedures for using tools in the Points toolbox including examples are presented in this chapter in the order in which the tools appear on the pul...

Page 49: ... point 1 Select Point from the Points toolbox 2 Move the cursor to any location in the plane where you want a point When the cursor message appears click once to create a point If in free space a cursor message does not appear Note You do not have to select the Point on Object or Intersection Point s tools to create a point on an object or at an intersection Create points in free space Create poin...

Page 50: ...n Object tool creates points on any object Creating a point on an object 1 Select Point on Object from the Points toolbox 2 Move the cursor toward the object until a cursor message appears for that object and then click once Point Click Modifying a point on an object Move a point by dragging it to a new location The point always remains on the object On this polygon ...

Page 51: ...pears If this happens hold down the mouse button and select the correct object from the list If you change the objects so that they no longer intersect the intersection point s disappears but reappears if the objects intersect again Creating an intersection point 1 Select Intersection Point s from the Points toolbox 2 Select two intersecting objects Select the first object Select the second object...

Page 52: ...ws the location of the Lines toolbox on the Cabri Geometry II toolbar along with its pull down menu Procedures for using tools in the Lines toolbox including examples are presented in this chapter in the order in which the tools appear on the pull down menu Defined objects in Cabri Geometry II such as triangles and polygons can be translated rotated or dilated Refer to the chapters Using the Point...

Page 53: ...or select the initial point of the line 3 Specify the slope by positioning the line in the desired orientation and clicking When specifying slope you can create a point on an object select an existing point or click in unoccupied space Create a point Specify the slope Modifying a line Translate a line without changing the slope by selecting the Pointer tool from the Pointer toolbox Then using the ...

Page 54: ...t grab the line away from the point and drag Press the SHIFT key to constrain the slope to 15 degree increments 4 To change a line constructed with two basic points drag either of the points 4 Changing a line constructed with a dependent point is relative to the object to which it is attached You may drag the object or the point depending on the construction Example Create a point Create a point T...

Page 55: ...ck to create or select the initial endpoint of the segment Create the initial point 3 Move the pointer to the location for the final endpoint of the segment and click to create or select the final endpoint Create the final point Example Select the initial point Point to the object Create the final point Note See Regular Polygon in this chapter for more information on creating the regular pentagon ...

Page 56: ... is not in free space it is attached to a second point Click to specify the slope Modifying a ray Translate a ray without changing its direction and slope by selecting the Pointer tool from the Pointer toolbox Then using the Pointer 4 For a ray constructed with a single point drag the point 4 For a ray constructed with two basic points grab the ray away from the points and drag Change the directio...

Page 57: ...final endpoint Creating a vector 1 Select Vector from the Lines toolbox 2 Click to create or select the tail of the vector Create the tail 3 Move the pointer to the location for the head and click to create or select the head of the vector Create the head Modifying a vector Change a vector by dragging either endpoint Translate a vector constructed with two basic points by grabbing the segment away...

Page 58: ...ngle 1 Select Triangle from the Lines toolbox 2 Click to create or select the initial vertex Create the first vertex 3 Move the cursor from the initial vertex and then click to create the second vertex Repeat to create or select the final vertex Create the second vertex Create the final vertex Modifying a triangle Move a triangle as an object by dragging one of its sides Change a triangle by dragg...

Page 59: ...ating a polygon 1 Select Polygon from the Lines toolbox 2 Click to create or select the initial vertex 3 Move the cursor from the initial vertex and then click to create or select the other vertices To terminate polygon construction double click or select the initial vertex Create the initial vertex Create additional vertices Modifying a polygon Move a polygon as an object by dragging one of its s...

Page 60: ...nt Create the center point 3 Move the cursor from the center point and click to specify the radius of a regular polygon The number of sides is displayed at the center point Specify the size 4 To create a regular convex polygon move the cursor clockwise from its current position To create a regular star polygon move the cursor counterclockwise and click when the regular polygon is the desired size ...

Page 61: ...d Modifying a regular polygon Move a regular polygon as an object by dragging one of its sides Change a polygon by dragging any of its vertices Dragging the center point changes the size of the regular polygon since the original vertex is anchored location dependent Example 1 Create the center point 2 Specify the size 3 Rotate counter clockwise 4 7 3 star polygon ...

Page 62: ...tures in Cabri Geometry II These features allow you to create curved objects including ellipses parabolas and hyperbolas The illustration below shows the location of the Curves toolbox on the Cabri Geometry II toolbar along with its pull down menu Procedures for using tools in the Curves toolbox including examples are presented in this chapter in the order in which the tools appear on the pull dow...

Page 63: ... Curves toolbox 2 Create or select the center point of the circle Create the center point 3 Move the cursor from the center point and click once to set the radius If you click in free space a point is not created You can also create or select a point Specify the radius Modifying a circle To translate a circle without changing its radius the circle must be constructed with a single point Drag the p...

Page 64: ...rc from the Curves toolbox 2 Create or select the initial endpoint of the arc Create the initial point 3 Move the cursor from the initial endpoint and click to create or select the curvature point 4 Move the cursor from the curvature point and click to create or select the final endpoint Create the second point Create the final point Modifying an arc Change an arc by dragging any of its three poin...

Page 65: ...ement of three points the conic is drawn to aid you in placing the remaining points Create three points Shape with the fourth point Complete with the fifth point Modifying a conic Move a conic by grabbing it away from its defining points and dragging it to a new location If any of the points are dependent the conic also changes Modify the conic by dragging any of its five points Note Depending on ...

Page 66: ... allow you to construct objects in relation to other objects The illustration below shows the location of the Construct toolbox on the Cabri Geometry II toolbar along with its pull down menu Procedures for using Construct tools including examples are presented in this chapter in the order in which the tools appear on the pull down menu Perpendicular Line Parallel Line Midpoint Perpendicular Bisect...

Page 67: ...ide of a polygon that will be perpendicular to the constructed line and click to select Select a linear object 3 Click to create or select the point through which the perpendicular line will pass Note The order of steps 2 and 3 may be reversed Select a point A dependent line is created Modifying a perpendicular line Move a perpendicular line by dragging the point through which it passes The line c...

Page 68: ...vector or side of a polygon that will be parallel to the constructed line and click to select Select a linear object 3 Designate the point through which the parallel line will pass Note The order of steps 2 and 3 may be reversed Select a point A dependent line is created Modifying a parallel line Move a parallel line by dragging the point through which it passes The line cannot be altered directly...

Page 69: ...point tool creates a point at the midpoint of a segment or vector the side of a polygon or between two points Creating a midpoint 1 Select Midpoint from the Construct toolbox 2 Point to one of the following and click to select Two points create or select A segment The side of a polygon Modifying a midpoint Modify a midpoint by modifying its defining objects ...

Page 70: ... and passes through the midpoint of the selected object Creating a perpendicular bisector 1 Select Perpendicular Bisector from the Construct toolbox 2 Point to one of the following and click to select A segment or a vector The side of a polygon Two points create or select Modifying a perpendicular bisector A perpendicular bisector cannot be translated directly unless it is constructed between two ...

Page 71: ...ough which the line passes Creating an angle bisector 1 Select Angle Bisector from the Construct toolbox 2 Click to create or select three points that define the angle to be bisected The second point selected is the vertex of the angle Select points A B and C Select points B C and A Modifying an angle bisector An angle bisector cannot be translated directly unless it is defined by three independen...

Page 72: ... tail and may also be previously defined vector sums Creating a vector sum 1 Select Vector Sum from the Construct toolbox 2 Point and click to select any two vectors Select the first vector Select the second vector 3 Click to create or select the initial point for the resultant vector Select a tail point for the vector sum Modifying a vector sum A vector sum cannot be modified directly Modifying e...

Page 73: ...distance between two points Creating a circle using Compass 1 Select Compass from the Construct toolbox 2 Create or select two points or select a segment to define the radius of the circle Select a segment 3 Create or select the center point of the circle Select a center point Modifying a circle created using Compass Modify the radius by dragging one of the defining endpoints Translate the compass...

Page 74: ...d to units Creating a measurement transfer 1 Select Measurement Transfer from the Construct toolbox 2 Point to any measurement or numerical value and click to select 3 To construct 4 a point at a proportional linear distance select a ray vector polygon or point If you select a point a dotted line appears Position the dotted line as you want it and click to set the position 4 a point at a proportio...

Page 75: ...nstruments Incorporated Measurement Transfer Continued Example Select a numerical value Select a point Position the point and click The points are 2 5 cm apart Modifying a measurement transfer Modify the constructed point by changing the measurement or numerical value The point cannot be translated directly This number ...

Page 76: ...ou can change this setting using Preferences in the Options menu Choices for connecting locus points and constructing the envelope of a line are also available under Preferences See Options Menu in the chapter Using the Menus for more information As an alternate method for changing the number of objects that define the locus you can select the locus and then press or to increase or decrease the nu...

Page 77: ...included 1997 1999 Texas Instruments Incorporated Locus Continued Modifying a locus Modify a locus by changing its defining objects Example Construct an ellipse conic Attach a segment to a new point on the ellipse Take the locus of the segment as one of its endpoints travels around the ellipse ...

Page 78: ...ect Redefine Point from the Construct toolbox 2 Press and hold the mouse down on any point A dialogue box appears with the following options 4 Point redefines the point as a basic point at the same location 4 Point on Object redefines the point to be on an object 4 Intersection Point s redefines the point to be at the intersection of two objects 4 Transfer to another point transfers the point to a...

Page 79: ...se on the object and then select the new definition 4 Circle Triangle Segment etc lets you construct a new object of the same type and automatically transfer the original object to it 4 Transfer to another object transfers and merges the object to another existing object of the same type A pop up menu appears with the following options 2c If the object is a line hold the mouse on the line and then...

Page 80: ...es These features allow you to translate reflect rotate and dilate objects according to specified factors and angular values The illustration below shows the location of the Transform toolbox on the Cabri Geometry II toolbar along with its pull down menu Procedures for using Transform tools including examples are presented in this chapter in the order in which the tools appear on the pull down men...

Page 81: ...1 Select Reflection from the Transform toolbox 2 Select the object to reflect Select the object to reflect 3 Select the line segment ray vector axis or side of a polygon to reflect the object across Select the linear object The reflected object is created Modifying a reflection Change the reflected image by changing the original object or by modifying the line of reflection Because it is a depende...

Page 82: ...cal image 1 Select Symmetry from the Transform toolbox 2 Select the object to reflect 180 degrees Select the object to reflect 3 Select the point of symmetry Select a point The symmetric image is created Modifying a symmetrical image Change a symmetrical image by changing the original object or by moving the point of symmetry Because it is a dependent object you cannot change a symmetrical image d...

Page 83: ...lbox 2 Select the object to translate Select the object to translate 3 Select the vector that defines the translation direction and distance Select the translation vector The translated image is created Modifying a translation Move a translated image by dragging the vector head or tail to a new location The translated image changes according to the changes of the vector or changes to the original ...

Page 84: ...ease refer to Numerical Edit in the chapter Using the Display Toolbox Rotating an object 1 Select Rotation from the Transform toolbox 2 Select the object to rotate Select the object to rotate 3 Select the point of rotation Select the rotation point 4 Select the angular value of rotation Modifying a rotation Change the rotated image by either modifying the figure that defines the angle of rotation ...

Page 85: ...ter Using the Display Toolbox Dilating an object 1 Select Dilation from the Transform toolbox 2 Select the object to dilate Select the object to dilate 3 Select the point of dilation Select the dilation point 4 Select the factor of dilation Select the dilation factor The dilated image is created Modifying a dilation Change the dilated image by either modifying the figure that defines the factor ed...

Page 86: ...o be on a line passing through the circle the locus of M constructs a circle that passes through the center of the circle If the original point lies in the interior of the circle the inverse point is constructed in the exterior and vice versa The inverse point lies on a ray with the center point as the endpoint Creating an inverse point 1 Select Inverse from the Transform toolbox 2 Create or selec...

Page 87: ...A macro is a sequence of interdependent constructions Macros are useful for creating new tools that construct unique objects or perform repetitive tasks The illustration below shows the location of the Macro toolbox on the Cabri Geometry II toolbar along with its pull down menu Procedures for creating macros including rules and examples are presented in this chapter in the order in which macros mu...

Page 88: ...not be defined as final objects You can select measurements and numerical values as final objects but any text attached will not be duplicated when the macro executes 4 The location of an arbitrary point on an object is determined by a random number generation Therefore the position of the point will be uncertain if it is selected as a final object 4 If the initial objects are different types for ...

Page 89: ...s needed to define the given conditions for a macro See Rules for creating macros for more information Specifying initial object s 1 Select Initial Object from the Macro toolbox 2 Click once to select an object The selected object displays in marquee outline 3 Optional Click again on the object to deselect it The object returns to its original outline Select initial objects Selected objects This t...

Page 90: ...at will result from the initial objects defined for a macro See Rules for creating macros for more information Specifying final object s 1 Select Final Object from the Macro toolbox 2 Click once to select an object The selected object displays in marquee outline 3 Optional Click again on the object to deselect it The object returns to its original outline Select final objects Select objects This c...

Page 91: ...ws DOS Name of the construction Enter a name for your construction or select a previously named macro To access a previously named macro point to the arrow on the right hand side of this field and press and hold the mouse button The name entered here will appear in the Macro toolbox when you select OK or OK and save Icon font Macintosh only The first letter of the construction name entered above a...

Page 92: ...ave to generate a save file dialog that allows you to save the macro to a file you specify Macros saved to individual files can be recalled in future constructions by using Open in the File menu to open the macro file Specifying a macro 1 Select Define Macro from the Macro toolbox 2 Enter the requested information into the dialog box to save your macro If you receive a warning message instead of t...

Page 93: ... check the validity of geometric properties in general Results are reported in text which can be edited with the Comments tool located in the Display toolbox The illustration below shows the location of the Check Property toolbox on the Cabri Geometry II toolbar along with its pull down menu Procedures for using Check Property tools including examples are presented in this chapter in the order in ...

Page 94: ...n text Checking collinearity 1 Select Collinear from the Check Property toolbox 2 Select any three existing points A marquee box appears after the last selection 3 Move the pointer to move this box anywhere in the drawing window and click to display the result If you change the points so that the property changes the displayed text changes accordingly Select three points Click to place the marquee...

Page 95: ...in text Check parallelism 1 Select Parallel from the Check Property toolbox 2 Select any combination of two lines segments rays vectors axes or sides of a polygon A marquee box appears after the last selection 3 Move the pointer to move this box anywhere in the drawing window and click to display the result If you change the objects so that the property changes the displayed text changes according...

Page 96: ...ext Checking perpendicularity 1 Select Perpendicular from the Check Property toolbox 2 Select any combination of two lines segments rays vectors axes or sides of a polygon A marquee box appears after the last selection 3 Move the pointer to move this box anywhere in the drawing window and click to display the result If you change the objects so that the property changes the displayed text changes ...

Page 97: ...quidistant property 1 Select Equidistant from the Check Property toolbox 2 Select any three points The first point selected is checked relative to the two remaining points A marquee box appears after the last selection 3 Move the pointer to move this box anywhere in the drawing window and click to display the result The text states whether or not the first point selected is equidistant from the se...

Page 98: ...ip 1 Select Member from the Check Property toolbox 2 Select a point 3 Select any object A marquee box appears after the selection 4 Move the pointer to move this box anywhere in the drawing window and click to display the result If you change the objects so that the property changes the displayed text changes accordingly Select a point and an object Click to place the marquee box The result change...

Page 99: ...n Cabri Geometry II These features allow you to perform different measurements and calculations The illustration below shows the location of the Measure toolbox on the Cabri Geometry II toolbar along with its pull down menu Procedures for using Measure tools including examples are presented in this chapter in the order in which the tools appear on the pull down menu Distance Length Area Slope Angl...

Page 100: ...r creating it by typing the text See Comments in the chapter Using the Display Toolbox for more information on adding a comment to a numerical value Measuring objects 1 Select Distance Length from the Measure toolbox 2 To measure 4 length perimeter or circumference select an object 4 distance select two points 4 radius select the center point and then the circumference Select an object The result ...

Page 101: ...ly after creating it by typing the text See Comments in the chapter Using the Display Toolbox for more information on adding a comment to a numerical value Checking area 1 Select Area from the Measure toolbox 2 Select the polygon circle or ellipse whose area you want to measure Select the object The result is displayed Moving measurements Reposition the measurement by selecting it with the Pointer...

Page 102: ...by typing the text See Comments in the chapter Using the Display Toolbox for more information on adding a comment to a numerical value Checking slope 1 Select Slope from the Measure toolbox 2 Select the segment ray vector or line whose slope you want to measure Select the object The result is displayed Moving measurements Reposition the measurement by selecting it with the Pointer tool and draggin...

Page 103: ... by using Numerical Edit in the Display toolbox You can add a comment to the measurement immediately after creating it by typing the text See Comments in the chapter Using the Display Toolbox for more information on adding a comment to a numerical value Checking angles 1 Select Angle from the Measure toolbox 2 If an angle mark is displayed on the angle select the angle mark to measure the angle Ot...

Page 104: ... 1 Select Equation Coordinates from the Measure toolbox 2 Select the point line circle or conic whose equation you want to find If multiple coordinate systems are present you must select the coordinate system before the equation is displayed Select an object The result is displayed Select a point to display its coordinates Modifying the equation or coordinates The equation is updated as you modify...

Page 105: ...any coordinate set by clicking on each value individually The calculation result is displayed in the result window You can drag the result to the Cabri Geometry II drawing window When you drag the result to the drawing window a tag identifying it as a calculation result is dragged along with it See the step for copying the result to the drawing window in the procedure Entering a calculation on pag...

Page 106: ...ates square of a number x2 sqr value Inv LN Calculates the natural antilogarithm ex exp value Inv LOG Calculates the common antilogarithm 10x 10 value SIN Calculates the sine sin value COS Calculates the cosine cos value TAN Calculates the tangent tan value Calculates the square root x sqrt value Raises a number to a power yx value1 value2 LN Calculates the natural logarithm base e The value used ...

Page 107: ...ue ceil value Ceil value Round to nearest integer ROUND value round value Round value Sine SIN value sin value Sin value Cosine COS value cos value Cos value Tangent TAN value tan value Tan value Arc Sine ARCSIN value arcsin value asin value ArcSin value Arc Cosine ARCCOS value arccos value acos value ArcCos value Arc Tangent ARCTAN value arctan value atan value ArcTan value Hyperbolic Sin SINH va...

Page 108: ...dow to copy the result to the drawing window Click again in the drawing window to place the result Enter an expression Select the button to display the result Editing a calculation 1 Select the result with the Numerical Edit tool On the Macintosh click on the Calc button You must point to the number You can also select the Calculate tool and double click the result composition to the edit window T...

Page 109: ... unless the full width of the column is visible Each row of the table is numbered sequentially in the first column on the left You can enter single values into the table when at least one object changes and you press the TAB key You can collect data automatically by selecting the table and then using Animation Data is stored in the table for each of the defined tabulation values at a rate relative...

Page 110: ...e At least one value must change before a new row is entered To tabulate values automatically first select the table and then animate the construction using Animation or Multiple Animation in the Display toolbox When selected the table displays with a marquee rectangle around it Drag rectangle to size the table Click on each value to be tabulated Press the TAB key to tabulate entries Adding values...

Page 111: ...r 3 Drag the column to modify its width Deleting a column 1 Click in the first row of a column the title column to select the column The column is highlighted 2 Press DELETE or select Clear in the Edit menu to delete the column Deleting a row 1 Click in a row of the first column the sequentially numbered column to select the row The row is highlighted 2 Press DELETE or select Clear in the Edit men...

Page 112: ...metry II These features allow you to annotate your constructions or animate objects The illustration below shows the location of the Display toolbox on the Cabri Geometry II toolbar along with its pull down menu Procedures for using Display tools including examples are presented in this chapter in the order in which the tools appear on the pull down menu Label Comments Numerical Edit Mark Angle Fi...

Page 113: ...re already as you desire continue to step 4 If not select the font size style and color of the text to be entered Press and hold the mouse button while pointing to the small icon boxes at the top of the edit box The C S F and color block change the character font the character size the font style and the character color 4 Type the label text on the keyboard Select a point line or circle Enter a la...

Page 114: ... Draw toolbox Creating a comment 1 Select Comments from the Display toolbox 2 Drag a marquee rectangle to specify the location and line length of the comment in the drawing An edit box appears when you release the mouse button 3 If the attributes are already as you desire continue to step 4 If not select the font size style and color of the text that you want Press and hold the mouse button while ...

Page 115: ...it a comment by selecting it with the Comments tool An edit box appears You must shade text that you want to modify before making changes to its font size style or color Shade the text by dragging the I across it Then select the appropriate option Click directly on a numerical value within a comment to change its characteristics The options in the edit box change to the options available in Numeri...

Page 116: ... from the Display toolbox 2 Click to place an edit box anywhere in the drawing for creating an interactive number 3 If the attributes are already as you desire continue to step 4 If not select the font size style and color of the text that you want Press and hold the mouse button while pointing to the small icon boxes at the top of the edit box The C S F and color block change the character font t...

Page 117: ...to the cursor position and to the direction indicated by the Animation tool You can change the units of a numerical value or its displayed precision Using the Numerical Edit tool select the numerical value Select the U Macintosh in the edit box or press CTRL U Windows and DOS and assign a unit to any number or change to the desired units Cabri Geometry II performs unit conversions based on the num...

Page 118: ...t be the vertex Note To measure an angle just select the marked angle with the Angle tool in the Measure toolbox Select three points Drag the mark through the vertex to measure the reflex angle Modifying an angle mark Using the Pointer tool modify an angle mark by dragging it through the vertex to measure the opposite angle The angle mark changes to when the angle is 90 degrees Using the Modify Ap...

Page 119: ...ed Fixing or freeing points 1 Select Fix Free from the Display toolbox All fixed points are displayed with a thumb tack next to them 2 Select any free point to fix its location or any fixed point to free the location constraint The Fix Free tool works as a toggle function on a point To free all fixed points simultaneously click in free space while pressing SHIFT Select any point to fix its positio...

Page 120: ...h Drawing in the Edit menu Tracing an object 1 Select Trace On Off from the Display toolbox 2 Select the object to trace Selected objects are displayed in marquee outline 3 Disable the trace on an object by selecting the object displayed in marquee outline The Trace On Off tool works as a toggle function on an object To disable a trace on all objects simultaneously click in free space while pressi...

Page 121: ...x Animating an object 1 Select Animation from the Display toolbox 2 Place the cursor on any object and drag the animation spring in the opposite direction to the intended animation The farther away the spring is pulled the faster the object is animated The animation begins when the mouse button is released and the spring collapses If the Pointer tool is visible in the toolbar and the object does n...

Page 122: ...n the chapter Using the Measure Toolbox Using Multiple Animation 1 Select Multiple Animation from the Display toolbox 2 Place the cursor on any object and drag an animation spring in the opposite direction to the intended animation Select as many objects as desired for the animation Redefine any animation spring by selecting the object again The farther away the spring is pulled the faster the obj...

Page 123: ...I These features allow you to change the appearance of objects or display the coordinate system The illustration below shows the location of the Draw toolbox on the Cabri Geometry II toolbar along with its pull down menu Procedures for using Draw tools including examples are presented in this chapter in the order in which the tools appear on the pull down menu Hide Show Color Fill Thick Dotted Mod...

Page 124: ... object you want to hide Note Hidden objects are shown in dotted outline when the Hide Show tool is active otherwise they are invisible Pressing the OPTION key Macintosh or the CTRL key DOS filters the cursor messages for all hidden objects allowing easier access to visible objects 3 Select a hidden object to make it visible again Pressing SHIFT and clicking in free space makes all hidden objects ...

Page 125: ...to one of 15 colors in the color palette This tool does not display on black and white systems Changing the color of an object 1 Select Color from the Draw toolbox 2 Select one of the colors in the color palette The selected color appears outlined in the palette 3 Select any object to change its color to the color you selected Select a color from the palette Select object to change its color ...

Page 126: ...ll from the Draw toolbox 2 Select one of the colors patterns appear on black and white systems in the color palette Select a fill color from the palette 3 Select an object Select object to fill with color Modifying a filled object Select an object a second time with the same color to change the color to transparent white the original fill color Select an object a second time while pressing the OPT...

Page 127: ...ded 1997 1999 Texas Instruments Incorporated Thick The Thick tool changes the outline thickness of an object Changing outline thickness 1 Select Thick from the Draw toolbox 2 Select the thickness for the outline Select the thickness attributes 3 Select the object to be outlined Select an object ...

Page 128: ...cluded 1997 1999 Texas Instruments Incorporated Dotted The Dotted tool changes the outline pattern of an object Changing outline pattern 1 Select Dotted from the Draw toolbox 2 Select the pattern for the outline Select the outline attribute 3 Select the object to be outlined Select an object ...

Page 129: ...oints small medium large circular or cross 4 Angle marks one two or three tick marks 4 Segments zero one two or three tick marks 4 Coordinate system Cartesian or polar coordinates Polar coordinates can be represented in degrees gradients or radians 4 Comments transparent without border opaque without border transparent with border or opaque with border 3 Select the object you want to appear with t...

Page 130: ...axes 1 Select Show Hide Axes from the Draw toolbox 2 Coordinate system translation Drag the origin to translate the axes to a new location 3 Axes rotation Rotate both axes simultaneously by grabbing the x axis beyond the first scale mark and dragging in a circular manner Rotate the y axis separately by grabbing the y axis beyond the first scale mark and dragging in a circular manner Note Pressing ...

Page 131: ...the scale is defined in one centimeter increments You can define multiple coordinate systems Equations and coordinates and grids must be specified relative to a specific coordinate system if multiple coordinate systems are defined After defining a new coordinate system you can manipulate it in the same manner as the default coordinate system documented in the previous tool Show Hide Axes Creating ...

Page 132: ...orated Define Grid The Define Grid tool displays the grid of a defined coordinate system Defining and deleting a grid 1 Select Define Grid from the Draw toolbox 2 Select the coordinate system to display the grid 3 Delete the grid by selecting one of the grid points and pressing DELETE Click to select the coordinate system These axes ...

Page 133: ...ram 2 4 Collinear tool 10 2 Color tool 13 3 column width pointer 1 10 Comments tool 12 3 Compass tool 7 8 configuring memory setting 1 5 number of objects 1 5 number of screen colors 1 5 toolbar tools 2 9 Conic tool 6 4 constraining the slope of a line 5 2 Construct toolbox 7 1 constructing objects 1 10 construction pencil pointer 1 10 Copy command 2 5 creating angle bisectors 7 6 arcs 6 3 axes 13...

Page 134: ...4 Fill tool 13 4 filling an object with color 13 4 Final Object tool 9 4 Fix Free tool 12 8 fixing or freeing points 12 8 Font command 2 11 freehand rotation of an object 3 5 function buttons calculate window 11 8 functions and syntax calculate window 11 9 G grasping hand pointer 1 10 H Help menu 2 12 Hide Show tool 13 2 hiding and showing objects 13 2 I I beam pointer 1 10 Initial Object tool 9 3...

Page 135: ...configuration 1 4 Options menu 2 7 through 2 10 P Page Setup command 2 3 2 4 paint brush pointer 1 10 paint bucket pointer 1 10 paper size and orientation 2 3 2 4 Parallel Line tool 7 3 Parallel tool 10 3 Paste command 2 5 Perpendicular Bisector tool 7 5 Perpendicular Line tool 7 2 Perpendicular tool 10 4 Point on Object tool 4 3 Point tool 4 2 Pointer tool 3 2 Pointer toolbox 3 1 pointers display...

Page 136: ... checking 1 5 storing a macro in memory 9 2 9 5 Style command 2 11 2 12 Symmetry tool 8 3 system requirements 1 2 T table dimensions using Tabulate 11 11 Tabulate tool adding values 11 12 description 11 11 sizing and deleting columns 11 13 using tabulate 11 12 Thick tool 13 5 Tool Configuration command 2 9 Toolbar description 1 7 toolboxes Check Property 10 1 Construct 7 1 Curves 6 1 Display 12 1 ...

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