Cabri Geometry II Getting Started
Contents
1. Ai TEXAS INSTRUMENTS Getting Started with Cabri Geometry II for Macintosh Windows and MS DOS Important Texas Instruments makes no warranty either expressed or implied including but not limited to any implied warranties of merchantability and fitness for a particular purpose regarding any programs or book materials and makes such materials available solely on an as is basis In no event shall Texas Instruments be liable to anyone for special collateral incidental or consequential damages in connection with or arising out of the purchase or use of these materials and the sole and exclusive liability of Texas Instruments regardless of the form of action shall not exceed the purchase price of this equipment Moreover Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party Permission to Print Permission is hereby granted to teachers to reprint or photocopy in classroom workshop or seminar quantities the pages or sheets in this work that carry a Texas Instruments copyright notice These pages are designed to be reproduced by teachers for use in their classes 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 Instrum2. Click once the text box appears It may take more time than you expect for the text box to appear Type the name of the first friend Note You can resize the text box by dragging the bottom right corner Move the I which changes to a toward another point until it changes back to an and the message This point appears Click once Type the second name in the text box Repeat for the other friends Note You can use the Pointer tool first button to drag the labels for better visibility Getting Started with Cabri Geometry Il t Latai Comments Mumsriral Coie Mark negin Fin Free Tree nii nanas Meblinie Animation j This point Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated Construct the line segments to represent the handshakes 18 Select the Segment tool from the Lines toolbox third button 19 Move the 9 near a point representing a friend until the 9 changes to a and the message This point appears Click once Do not hold the mouse button Move the away from the point A line extends from the point Move the toward another point until the and the message This point appear Click again The line segment handshake is defined by the two end points friends Caution Do not click when the 9 is displayed with the message Point on this object because this will create a new point If you d
3. Ctrl Z Undo Undo the last action clipboard Bra fr meme aw CE Ctrl A Selectall Select all objects in the drawing Replays each step of a construction Ctrl F Refresh the drawing screen remove leftover Trace elements 38 Getting Started with Cabri Geometry II Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated Hide Show Attributes Hide the toolbar or display the toolbar that controls how objects look Preferences 0 Set preferences for how drawings are set up E Tool Configuration Rearrange or hide tools Macintosh Displays a description of the selected toolbar icon in the Help EU Windows DOS window at the bottom of the Cabri Geometry II screen Displays information about Cabri Geometry II that includes the authors names copyright notice and the version number of the software e To increase or decrease the displayed precision in Numerical Edit Press or e To increase or decrease the animation speed in Animation or Multiple Animation e To increase or decrease the number of objects in the selected locus e To limit the slope of lines rays segments vectors triangles polygons or axes to increments of 15 e To limit the radius to multiples of 1 cm when creating circles e To select multiple objects Press Tab Torecord new values in a table e To change the format of a selected equation Press Enter To start a Multiple Animation Press and
4. radius of a selected circle Copying permitted provided TI copyright notice is included Getting Started with Cabri Geometry Il 41 1997 1999 Texas Instruments Incorporated Toolbar Commands Continued Initial Object Specify the initial object s needed to define the final object s Final Object Specify the final object s that will result from the initial object s Define Macro Open the dialogue box for naming and saving the macro defined by the initial and final object s The macro is added to the Macro toolbox Report whether or not three selected points are on the same line f Parallel Report whether or not two selected lines segments rays vectors axes or sides of a polygon are parallel a T Perpendicular Report whether or not two selected lines segments rays e vectors axes or sides of a polygon are perpendicular Equidistant Report whether or not three selected points are equidistant e Report whether or not a selected point lies on a selected object i em a Distance amp Length Display the distance between two selected points or the length of a segment perimeter circumference or radius mm a Display the area of a selected polygon circle or ellipse Display the slope of a selected line segment ray or vector Display the measure of a marked angle or an angle defined by three selected points Equation amp Coordinates Display the coordinates of a point or the
5. Click on the OK button to save the macro The macro now appears in the Macro toolbox with the name Pentagram The macro will generate an inscribed regular polygon Getting Started with Cabri Geometry II ams of ihn renina on Tani HI F T Note Colors available in Windows version only Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated Test the Pentagonal Curve of Pursuit macro 24 Select the Pentagram macro from the Macro toolbox Point to p the inner regular pentagon until the message This polygon f appears Click to create a new inscribed pentagon within the ts selected pentagon Does the macro meet your criteria If not repeat the definition of initial and final objects and selection of attributes If problems still exist you may need to review the original construction again Continue to apply the Pentagram macro 25 Apply the macro Pentagram to the construction again Point to the new inner pentagon and click to create yet another pentagon Repeat until you have a construction similar to the illustration Note As your construction gets more and more crowded you can rely on the ambiguity feature of Cabri II to select the pentagon created last That is the pointer may appear E along with the message Which object Press and hold the mouse to see a list of the objects available Point to the last object in the list which is the last object c
6. The attribute icons appear vertically on the left side of the drawing screen These icons represent tools that let you control the appearance of objects that you create SEXE EHE FFE Le 13 The fourth attribute icon represents the currently selected Point attribute Click and hold the button to display the choices You can construct a point as ae e O or x e a a IE x select the O attribute Now every point that you construct with the Point tool will appear on the drawing screen as a O until you change the attribute changes appearance and the message On this circle appears This message tells you that the defined point will be attached to the circle and that if you move the circle the point will move with it 14 Move the toward the circumference until the pencil B On this circle Click to create a O to represent the first friend 15 Add the other three friends in the same way evenly spaced around the circle To check your work complete the Checkpoint 1 instructions on the next page Copying permitted provided TI copyright notice is included Getting Started with Cabri Geometry l 13 1997 1999 Texas Instruments Incorporated Modeling Handshakes Continued Write the name of a friend next to each point 16 17 14 Select the Label tool from the Display toolbox tenth button Move the toward one of the points until it changes to an I beam and the message This point appears
7. These include color line thickness line appearance point type and others Note On monochrome systems the color palette is not available On these systems the palette presents varied shades of gray You can drag the palette by its title bar to a more convenient location on the drawing window You can close any unneeded attribute toolbox by clicking on the close box at the left corner of that toolbox 1997 1999 Texas Instruments Incorporated Add the fifth friend and handshakes 23 Select the Point tool from the Points toolbox second button Pat Notice that O and the color red are selected on the palette Each time you select a new tool the palette shows the current settings for that tool Danny Michell 24 Select a different color and x as the Point Attributes for the fifth friend Then add the new friend to the circle Select Label from the Display toolbox tenth button Move to the new point click once and type the friend s name You can use the Pointer tool first button to enlarge the circle and Mike reposition the points and labels as needed for visibility Dianna Note You can label a point when you create it by typing the name on the keyboard immediately after creating the point However this labeling method is limited to five characters 25 Select the Segment tool from the Lines toolbox third button Choose a different color and a different Line Attribute such as a dotted line or a heavier
8. toward point S until the message This point appears Click once to create the initial end point of the segment Move the toward one of the intersections of line and circle until the message Point at this intersection appears Click to complete the segment construction Repeat this procedure to construct a segment on the other line 26 Getting Started with Cabri Geometry Il This peint Point at this intersection Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated Label the points 10 Select the Label tool from the Display toolbox tenth button Move the toward one of large points on the circle until the changes to I I beam and the message This point appears Click once An edit window appears next to the point Enter the label from the keyboard Call this point A Move the I toward the small point which is on the same line Click once to open the edit window Call this point B 11 Repeat step 10 for the two unlabelled points on the circle labeling them C and D Hide the lines 12 Hiding objects can often make a construction easier to read visually as well as add an element of intrigue Hiding the lines will aid you in evaluating the intersecting chords Select the Hide Show tool from the Draw toolbox last button Notice that the construction is redrawn quickly 13 Move the toward a line until the message This line appears Click once The line b
9. Move the toward the polygon until the message Rotate this polygon appears Click to select the polygon 31 Move the toward the origin point until the message around this point appears Click to select this point Now move the 9 toward the value 30 until the message using this angle appears Click to select the value An image of the polygon that is rotated 30 degrees around the origin point is created Dynamically change the rotation angle 32 Select the Numerical Edit tool from the Display toolbox tenth button Move the I I beam towards the value 30 degrees until the message This number appears Click once to select the value A flashing cursor appears in the window next to the number 33 Press the lt left arrow key on your keyboard to position the flashing cursor to the right of the 3 Now press the T up arrow key Notice that the first digit increases by 1 The Numerical Edit tool increases decreases the digit to its left when the up and down arrow keys are used Press the T up arrow key until the value reads 90 degrees noticing the changes in the rotated polygon Now press the 4 down arrow key The digit decreases by 1 You can change the rotation angle dynamically to any value using this method Alternatively you can highlight the value using the mouse and type in a new value Dilate the polygon by a defined factor 34 You also can dilate a polygon by a factor that you define This example begins w
10. Segment Division macro 1l Draw another segment using the Segment tool from the Lines toolbox third button Then select the Segment Division macro from the Macro toolbox seventh button Move the toward the segment until the message This segment appears Click once The point that appears on the segment is located one eighth of the length of the segment from the second end point e a Note Macros follow the order of the original construction Construct another segment If you constructed the segment i from left to right last time construct it from right to left this time Then apply the Segment Division macro Notice that the macro places the point closest to the second end point created This is consistent with how the macro was defined Construct a regular pentagon 12 Select the Regular Polygon tool from the Lines toolbox third button Move the to an empty section of your drawing window Click to create the center point of the regular polygon en 13 Move the cursor away from the center point noticing that a polygon appears Click to specify the radius of the regular polygon Make your radius about 3 or 4 cm The number of sides of the regular polygon is displayed at the center point RTS 34 Getting Started with Cabri Geometry Il Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated 14 Now move the in a clockwise direction The number of sides de
11. current construction if one exists Construct a circle 2 Select the Circle tool from the Curves toolbox fourth button To construct a circle move the and then click once to create the center point Move the mouse away The outline of the circle is drawn Click again to specify the radius of the circle Construct a point that lies within the circle 3 Select the Point tool from the Points toolbox Second button Move the 9 to a location inside the circle Click once to create a point Then type the letter S from the keyboard Construct two lines that intersect at S 4 Select the Line tool from the Lines toolbox third button Move the 8 toward the circle until the and the message On this circle appear Click once The initial point of the line appears Move the cursor toward the point S until the message By this point appears Click once to attach the line to the point and complete the definition of the line Repeat this procedure to construct another line attached to the circle that intersects the first line at S Note The intersection point S is a basic object That is it can be moved freely about the construction The two points that are attached to the circle are ndependent points Independent points can be moved with respect to the object to which they are attached These types of points are in contrast to dependent points which cannot be moved directly For a complete discussion of basic independent and depend
12. equation of a line circle or conic Open the calculator to perform calculations using measurements numerical values calculation results or numerical inputs from the keyboard 42 Getting Started with Cabri Geometry II Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated may contain text and numbers A Comments Enter a comment in the drawing The comment window is defined by location and size Numerical Edit Edit any measurement coordinate or equation the value 2 a 1 precision units font size and style may be modified Mark Angle Place an angle mark on an angle defined by three points the LL second of which is the vertex Fix Free Fix the location of a point Free a fixed point Trace On Off Trace a selected object along a specified path v Quit tracing Automatically translate rotate or dilate an object in the ye direction specified by the animation spring Click once to stop the animation Multiple Animation Animate multiple objects along multiple paths Label Attach a user created label to a point line or circle The label Show Axes Show the default coordinate system for coordinate geometry Hide Axes Hide the default coordinate system Create a coordinate system by defining a point for the origin a x point for the x axis and a point for the y axis Define Grid Display a grid for the selected axes Copying permitted provided TI copyright notice
13. hold the mouse key To display all directly moveable basic and independent objects as flashing The cursor must be in an unoccupied space Press Ctrl and drag the mouse To scroll the drawing window Double click the mouse key On a label comment numerical value or table to invoke the appropriate editor Click the mouse key Anywhere in the gray area of the Toolbar to access the Pointer tool Ctrl U Displays list of units in a pop up menu when the Numerical Edit tool is selected Copying permitted provided TI copyright notice is included Getting Started with Cabri Geometry l 39 1997 1999 Texas Instruments Incorporated Toolbar Commands De Pointer Select move and manipulate objects th Rotate Rotate an object around a selected point or the object s geometric center a 3 Expand or contract an object around a selected point or the S ot object s geometric center th Rotate and Dilate Simultaneously rotate and dilate an object around a selected point Lu or the object s geometric center Construct a point defined in free space on an object or at the intersection of two objects Point on Object Construct a point defined on an object Intersection Point s Construct a point at each intersection of two selected objects Construct an infinite line through a point at a slope specified by clicking a second time in free space or at a point Construct a segment defined by two end points which may be created or d
14. permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated He LS ls le aj d Hi ny sai EN D _ i Circle Arc Conic Conic Arc a a Seed 2127 ae Getting Started with Cabri Geometry ll 11 Modeling Handshakes Continued Move and resize the circle 6 Instead of making another circle practice moving and resizing the circle The tools for moving and resizing are in the Pointer toolbox which is the first toolbox on the toolbar Begin by pulling down the Pointer toolbox then point to and select the Pointer tool X T Move the X into the drawing window Notice that the X changes to a cross hair Move the to the point at the center of the circle It changes to a pointing hand and the message This point appears Cabri Geometry II recognizes all the objects you create and informs you when the cursor is close enough to an object for you to select it or perform some other activity Click once on the mouse button The point flashes indicating that the point is selected 8 Click and hold the mouse button The changes to a i grasping hand to show that you can move the object While holding the mouse button down drag the point toward the right to move the circle Release the mouse button Note You don t have to select a point to move it 9 Now move the away from the center
15. point It changes back into a Move the toward the circumference until it changes to the with the message This circle Click once on the mouse button Do not hold the mouse button down The circumference appears to be moving or flashing This marquee outline indicates that the circumference is selected To deselect the circle move the until it changes to a and then click The circumference no longer appears to be moving 10 Move the near the circumference until the 5 appears Click and hold the mouse button The changes into a amp Enlarge the circle to fill the screen by dragging the circumference Release the button 12 Getting Started with Cabri Geometry Il DITI Sd Pointer p Rotate Dilate Rotate and Dilate PEE T 7 4 E This circle A Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated Construct points to represent the four friends 11 The second button on the toolbar shows the currently Ha 2d bx selected tool in the Points toolbox Pull down the Points menu Point k and select the Point tool Point on Object Intersection Pointis 12 Pull down the Options menu above the toolbar Select Show Options Attributes Macintosh Windows Hide Show Attributes DOS PUE TED PTauits Preferences Macintosh and Tool Configuration Windows only m EN Language Font d Size Style d
16. research and thesis have been devoted to the use of technology in the classroom Cabri Geometry Il Features e Includes interactive analytic transformational and Euclidean geometry e Allows intuitive construction of points lines triangles polygons circles and other basic objects e Translates dilates and rotates geometric objects around geometric centers or specified points plus reflection symmetry and inverse of the objects e Constructs conics easily including ellipses and hyperbolas e Explores advanced concepts in projective and hyperbolic geometry e Annotates and measures figures with automatic updating e Uses both Cartesian and polar coordinates e Provides for user display of the equations of geometric objects including lines circles ellipses and coordinates of points e Allows the user to create macros for frequently repeated constructions e Lets the teacher configure tool menus to focus student activities e Checks geometric properties to test hypotheses based on Euclid s five postulates e Hides objects used in constructions to reduce screen clutter e Differentiates objects through the use of paint like color and line palettes e Computes a locus continuously e Illustrates the dynamic characteristics of figures through animation e Allows the user to save drawings and macros to disk e Opens geometry constructions created on the TI 92 e Provides one square meter of full size work space and pr
17. the Pointer tool to reposition the area measurement so that you can see the measurement as you transform and 2 70 2 56 explore the triangle Lo 3 76 2 20 1 03 1 03 1997 1999 Texas Instruments Incorporated Transform and explore the triangle 8 10 11 Now use the Pointer tool to drag any one of the vertices Drag it into each of the other quadrants What happens to the coordinate values To the area Return the vertex to the upper right quadrant Move the toward a side of the triangle Because the triangle was created as an object the message This triangle appears Drag the entire triangle into each of the quadrants What happens to the coordinate values To the area Return the triangle to the upper right quadrant Select the Rotate tool from the Pointer toolbox first button Drag the triangle not a vertex moving the cursor in a circular motion The entire triangle rotates around its geometric center What happens to the area You also can rotate the triangle around a specified point With the Rotate tool selected move the to the origin until the and the message This point appear Click on the selected point The selected point begins flashing Move the cursor toward the triangle When the message This triangle appears drag the triangle in a circular motion around the origin What happens to the coordinate values Does the area change Why or why not Copying permitted provid
18. toolbox third button Construct a four sided polygon in the upper right quadrant by moving the 8 and clicking once at each vertex Make it any shape you want The last vertex must be the same as the first Click when the message This point appears Translate the polygon 22 You can translate an object according to a selected vector Select Vector from the Lines toolbox third button Move the and click once in the upper right quadrant to create the tail of the vector and move the 9 and click again to create the head of the vector 23 select the Translation tool from the Transform toolbox sixth button Click on the polygon when the message Translate this polygon appears and then click on the vector when the message by this vector appears The translated polygon appears offset from the original polygon by the direction and length magnitude of the vector 24 Drag the head of the vector when the cursor changes to and the message Translate this point appears The translated polygon follows the head of the vector 25 Using the Pointer tool from the Pointer toolbox first button drag the original polygon What happens to the translated polygon Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated Getting Started with Cabri Geometry Il 21 Exploring Transformations in the Coordinate Plane Continued Rotate a polygon by a defined angular value 26 You can r
19. 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 Discretes et de Didactique LSD2 a research laboratory within IMAG He graduated in mathematics at Ecole Normale Sup rieure in Paris in 1969 He earned a Ph D Th se d Etat in computer science at the University of Grenoble in 1977 Jean Marie began work on the Cabri II project in 1981 as an environment for graph theory He has devoted his research efforts to the use of geometric methods for the study of different classes of graphs especially hypercubes Franck Bellemain earned a Ph D in mathematics at the Universit Joseph Fourier in 1992 He began work on the Cabri IT 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 Il Features e Includes interactive analytic transformational and Euclidean geometry e Allows intuitive construction of points lines triangles polyg
20. Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated Installing Cabri Geometry Il on a network continued Macintosh and DOS 1 Install Cabri Geometry II on the network server using the instructions given on the previous page 2 Run the program from the server the first time and enter the requested information 3 To run Cabri Geometry II on each network client go to the directory on the network server where the Cabri Geometry II application is installed Macintosh users may double click on the Cabri II icon DOS users may run Cabri2 exe to start the program The procedure described below for Windows users allows multiple client computers to run Cabri Geometry II using the application software installed on the network server Each client computer is provided with the necessary system files to run Cabri Geometry II and a shortcut icon that is linked to the application file on the network server Windows 3 1 and Windows 95 1 Install Cabri Geometry II on the network server using the instructions given on the previous page In the Select Destination screen you must select a directory that will be accessible from each client computer on the network 2 Temporarily copy setup exe and setup w02 from the installation diskettes to the same directory in which you installed Cabri Geometry II in step 1 3 On each network client go to the directory on the network server that contains setup exe
21. EREEREERRRRERRRRRRRE LELEL EEOE L CAAZ OE 0 ZLZ CA A SE co E0O Z Z ZLA AA a E00SEEOEO 0 ZLZLAAAA C CA Seeder CEPCEECECELEEECEECEEEEECEDEPEEEEEEEEEEEPEEEEEEEEEEREREEEEEEPERE eee eee eee ee ene ee eee eee ene nae een sae sanenesaeseneaesausenesnusesesesnemeassal mm Getting Started with Cabri Geometry Il 31 Constructing a Macro Pentagonal Curve of Pursuit Problem Line designs created with colored thread can produce attractive patterns With Cabri II line designs are easy and fun Some designs can be developed by inscribing regular polygons within similar regular polygons This can be described as a series of two step transformations In this example we create a Pentagonal Curve of Pursuit by inscribing pentagons to illustrate some important features of macros Get ready 1 Start the software if necessary or select the New option from the File menu You will be prompted to save your current construction if one exists Construct a segment 2 Select the Segment tool from the Lines toolbox third button To construct a segment click once at each end point Construct a segment that is about 5 cm long Tip If you press the SHIFT key after creating the first end point the slope of the segment is limited to 15 degree increments Divide the segment into eighths 3 Select the Midpoint tool from the Construct toolbox fif
22. This section provides step by step exercises that give you hands on experience with several features basic to the construction of geometric objects using Cabri Geometry II To quickly learn Cabri Geometry II complete these four exercises Modeling Handshakes Use a circle points and line segments to model a real world problem for pattern recognition 11 Exploring Transformations in the Coordinate Plane Construct a triangle and explore reflection rotation and dilation around the x and y axes 18 Exploring Power Steiner of a Point Problem Construct a point as described by Euclid and then move the point to calculate various powers and record them inatable 25 Constructing a Macro Pentagram Create a pentagram by inscribing pentagons to illustrate some important features of macros 32 Menu Options and Toolbar Commands Menu Options Provides a quick reference and brief description of the menu options 38 Toolbar Commands Provides a quick reference to the tools available on each toolbar and a brief description about the operation of each tool 40 Note Most of the illustrations in this guidebook are from the Macintosh version of Cabri Geometry II several are from the Windows and DOS versions Due to space limitations we could not show every illus
23. and double click to on this file to run the setup program 4 In the Select Destination Directory screen click on the Browse button and select the same directory that you used in step 1 Make sure the correct directory is displayed at the top of the window You may edit the path if necessary and then click on OK Ignore the message that the directory already exists 5 In the Select Components screen deselect the first three components The installation program will determine if the fourth component is necessary for Windows 3 1x users 6 When Cabri Geometry II has been installed on all client computers delete the two files that were temporarily copied to the network server in step 2 Starting Cabri Geometry Il Macintosh DOS You can use one of four methods to start the Type CABRI and press ENTER from the DOS software on a Macintosh prompt directory where the Cabri Geometry II e Use Open in the Finder files are located Double click on the Cabri Il icon Optional Add the Cabri directory to your DOS Double click on any Cabri Geometry II p a to open Cabri Geometry Il from any directory construction file tool configuration file or macro file e Drag and drop any construction file onto the Cabri Il icon System 7 users only Windows Double click on the Cabri Il icon Cabri Il Copying permitted provided TI copyright notice is included Getting Started with Cabri Geometry l 7 1997 1999 Texas Instruments Incorpo
24. appears Click once to select the value A flashing cursor appears in the numerical edit window next to the number Use the left and right arrow keys on your keyboard as necessary to position the flashing cursor to the right of the 2 Press the t up arrow key until the value reads 2 0 Now press the V down arrow key until the value reads 1 0 You can change the dilation factor dynamically to any value using this method Alternatively you can highlight the value using the mouse and type in a new value Continue to explore by changing the numerical values in various ways and comparing them with other transformational methods in Cabri Geometry II 24 Getting Started with Cabri Geometry Il 12 en Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated Exploring Power Steiner of a Point Problem Problem A theorem which originally appeared in Euclid s Book III Proposition 35 states the following Given that a secant intersects a circle at A and B and that a second secant intersects the circle at C and D 4f the secants intersect at S then AS BS CS DS This property was investigated by the Swiss geometer Jakob Steiner 1796 1863 who first used the term power of the point for this product Get ready 1 Start the software if necessary or select the New option from the File menu if the drawing window is already displayed You will be prompted to save your
25. atible 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 95 386 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 DOS 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 95 1 Insert the Cabri Geometry II Windows diskette 1 in your floppy disk drive 2 Click on START RUN and enter A SETUP and then follow the screen prompts 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 6 Getting Started with Cabri Geometry Il
26. be the length of a segment which is included in the calculation although it is not visible in the table 30 There are several ways in which to approach this problem AS BS CS DS This step examines one possible observation You may wish m ee 233 ol 2232 12 Pr 4 93 4 93 i to explore other facets of the problem 3 Me rr ees E E fe Stes E CIN Drag point Sonan imaginary line through the center point z den 2 D visited 2 de of the circle Press the TAB key about every centimeter to 51 9082 508 c collect a new power of S calculation PNE LACS NS 192 Lj T BoE be 3 87 ia We D en Xi Me x Analyze the data 31 Notice that the powers of S are smaller the further away from the center point you move point S This is true as long as you keep point S within the circle The opposite occurs outside of the circle although the property continues to hold true Did any of the values repeat when you moved point S across the circle If necessary resize the table to view all of its contents Drag the table up the drawing window to see the lower rows 30 Getting Started with Cabri Geometry Il Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated Modify the table and delete values from the table 32 Select Tabulate from the Measure toolbox Point to the table and click An edit window encloses the table Point to the first column of a row and click The first column is the column
27. creases When the number of sides is five click to complete the construction of the regular polygon A regular pentagon is displayed If you move in a counterclockwise direction the number of sides becomes a fraction and the polygon drawn is a regular star polygon Apply the Segment Division macro 15 Select the Segment Division macro from the Macro toolbox i seventh button Move the toward a side of the regular polygon until the message This side of the polygon appears Click once to apply the macro A point is created on the side of the pentagon Repeat this step for each side of the pentagon Inscribe the regular pentagon p 16 Select the Polygon tool from the Lines toolbox third button Use the Polygon tool to connect the points created by the 1 Segment Division macro Proceed in a clockwise direction Do not connect the vertices of the regular pentagon Select each point When all of the points have been selected j select the first point again This terminates the polygon An inscribed regular pentagon is created Define a macro to create an inscribed regular pentagon 17 Select Initial Object from the Macro toolbox Select the outer regular pentagon as the initial object Move the toward the outer pentagon until the message This regular polygon appears Click once The pentagon is shown as a marquee outline Note Objects created by macros can be used to generate i other macros For example the
28. dicular Bisector Construct a perpendicular line bisecting two points a segment or side of a polygon Angle Bisector Construct a line that bisects an angle identified by three selected points the second point is the vertex tf Vector Sum Construct the sum of two vectors by specifying the vectors and the end point of the new vector mim Compass Construct a circle from a center point with radius defined by a segment or the distance between two selected points Measurement Transfer Create points on specific objects based on proportional or equivalent selected numerical values Locus Construct the locus of a single selected point or object defined by movement along a path Redefine Point Redefine a previously defined point to a new location Defining E Macintosh DOS a point in free space as on an object for example F Redefine Object Redefines a previously defined point object or line Windows IL Reflection Create the image of an object reflected across a line segment 5 ray vector axis or side of a polygon et Symmetry Create the image of an object rotated 180 around a point Create the image of an object translated by a specified vector E 7A Rotation Create the image of an object rotated around a point by a HE specified angular value Create the image of an object dilated from a point by a specified Y factor Inverse Create the image of a point by reflecting it inversely to the
29. draw a rectangle Release the mouse button A table appears within the rectangle If the size is unsuitable resize the table by dragging the lower right corner 28 Select the values you want to tabulate copy Move the 8 on top of the number you labeled as AS BS until the message Tabulate this value appears Click once to place it in the table for tabulation The label and the current value appear in the table Repeat this procedure for the value labeled CS DS If this value is not visible you must change the size of the table Only fully visible columns display results Resize the table by dragging the lower right corner Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated 45 29 om BS 1 43 em AS BS 3 93 om C5 4 25 em 5 71 20 em CS DS 3 93 om ha iHd E iL m ASS CSD 3 93 3 93 2 3 E Vn mal Getting Started with Cabri Geometry Il 29 Exploring Power Steiner of a Point Problem Continued Collect data to support the hypothesis 29 You may wish to record additional values to support the hypothesis Select the Pointer tool from the Pointer toolbox Drag the points A C and S to manipulate the construction as you wish Press the TAB key to record additional values in the columns defined Note At least one value must change in order for a new row of data to be recorded in the table In this case the value may
30. ecomes dotted Move to the other line and click It also becomes dotted These objects will be hidden from view when you change to another tool 14 Select the Pointer tool first button You now have a construction similar to the one investigated by Euclid over 2000 years ago Measure the lengths of the segments 15 Select the Distance amp Length tool from the Measure toolbox Move the toward segment AS until the message Length of this segment appears Click once to display the length of the segment Immediately after the measurement is created type AS from the keyboard The measurement is now labeled 16 Repeat step 15 for segments BS CS and DS You may need to adjust the positions of the displayed measurements in order to read them more easily Note Measurements also can be labeled using the Comments tool from the Display toolbox Select Comments Select the measurement Enter a label in the edit window Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated Getting Started with Cabri Geometry II 27 Exploring Power Steiner of a Point Problem Continued Measure the lengths of the segments continued 17 You may find it beneficial to group the measurements in one location in order to inspect the values easily Select the Pointer tool from the Pointer toolbox Drag each measurement to an unoccupied area of the drawing window The measurement will
31. ectangular coordinate axes y 2 Select Show Axes from the Draw toolbox last button The axes appear centered on the drawing screen Construct a triangle 3 Select the Triangle tool from the Lines toolbox third button To construct a triangle move the and click once at each vertex The lines are drawn automatically as you define the vertices Make the triangle any shape you want but put it in the upper right quadrant Display the coordinates for each vertex 4 Select the Equation amp Coordinates tool from the Measure y toolbox ninth button Move the 9 toward any vertex until the 5 and the message Coordinates of this point appear Click once The coordinates appear near the point Repeat for the remaining two vertices db dd Your coordinates may not match those shown here os 5 Reposition the coordinates for better visibility To do this TA eas select the Pointer tool from the Pointer toolbox first button Move the toward one pair of coordinates until you see the x message This number Drag the coordinates away from the triangle They momentarily resist but then let you position them anywhere on the drawing screen Repeat the process for the other coordinates Display the area of the triangle 6 Select Area from the Measure toolbox ninth button Move y the toward the triangle until the message This triangle appears Click once The area is calculated and displayed 1422 om 7 Use
32. ed TI copyright notice is included 1997 1999 Texas Instruments Incorporated 1 123 om 2 70 2 56 1 123 om 2 70 2 56 376 2 20 1 03 1 023 1 123 om 2 705 2 56 ri Z B lu f exo OTE 220 y 1 123 om 2 70 2 56 3 76 2 20 1 02 1 02 Getting Started with Cabri Geometry II 19 Exploring Transformations in the Coordinate Plane Continued Transform and explore the triangle continued 12 Select the Dilate tool from the Pointer toolbox first button Drag the triangle If the origin is still selected the triangle dilates toward and away from the origin What does this do to the shape and size of the triangle Deselect the origin by clicking in a blank part of the drawing screen Now dilate the triangle What happens this time The triangle dilates around its geometric center Explore reflections and symmetry 13 14 15 16 17 18 20 Drag the triangle back into the upper right quadrant if necessary Select the Reflection tool from the Transform toolbox sixth button To reflect the triangle across the y axis move the 9 until the message Reflect this triangle appears Click once Move the 9 to the y axis and click when the message with respect to this axis appears The reflected triangle appears in the upper left quadrant Select the Equation amp Coordinates tool from the Measure toolbox ninth b
33. efined in free space or on a defined object e Ray Construct a ray defined by an end point and direction extending infinitely _ Vector Construct a vector with magnitude and direction defined by two points i Triangle Construct a triangle defined by three points vertices which may be created or defined in free space or on a defined object uf d Polygon Construct an n sided polygon the last point must coincide with the beginning point Select or create a point for each vertex Regular Polygon Construct an n sided regular polygon Click for center and radius move clockwise convex or counterclockwise star to set n lt 30 A Construct a circle defined by a center point and a specified radius Construct an arc defined by an initial end point a radius point and a final end point ie Construct a conic ellipse parabola or hyperbola defined by five points 40 Getting Started with Cabri Geometry Il Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated de Perpendicular Line Construct a line perpendicular to a selected line segment ray j vector axis or side of a polygon passing through a created or selected point Parallel Line Construct a line parallel to a selected line segment ray vector axis or side of a polygon passing through a created or selected point Construct a midpoint of two selected points a segment or side of a polygon A Perpen
34. ent points and objects read Chapter 1 Basic Operations in the Cabri Geometry IT Guidebook Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated Q C I Getting Started with Cabri Geometry Il 25 Exploring Power Steiner of a Point Problem Continued Modify the appearance of the construction D Select the Modify Appearance tool from the Draw toolbox last button pop up screen showing the various appearance attributes appears Click on the large solid point in the top row If necessary point to the top line of the pop up screen and hold down the mouse button to drag the pop up screen away from your drawing Move the toward point S until the changes to a J and the message This point appears Click once The point changes to a large point Repeat this procedure for the two independent points Click on the close box in the top left corner of the pop up screen to remove the screen from the drawing window Construct segments within the circle 8 Select the Segment tool from the Lines toolbox third button Move the toward one of the independent points on the circle until the message This point appears Click once The initial end point of the segment appears Move the toward point S until the message This point appears Click to complete the segment construction Repeat this procedure to construct a segment on the other line Move the
35. ents Incorporated to reproduce or transmit this work or portions thereof in any other form or by any other electronic or mechanical means including any information storage or retrieval system unless expressly permitted by federal copyright law Address inquiries to Texas Instruments Incorporated 7800 Banner Drive Dallas TX 75251 M S 3918 Attention Manager Business Services TI Product and Services Information For more information about TI products and services contact TI by e mail or visit the TI calculator home page on the world wide web e mail address ti cares ti com internet address http www ti com calc Cabri Geometry II is a trademark of Universit 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 1997 1999 by Texas Instruments Incorporated All rights reserved Getting Started with Cabri Geometry Il for Macintosh Windows and MS D0S9 Dive into Geometry I TEXAS INSTRUMENTS About Cabri Geometry Il 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 Math matiques Appliqu es de Grenoble IMAG a research lab at the Universit Joseph Fourier in Grenoble France in cooperation
36. hesitate initially when being dragged but will then follow the pointer Calculate the power of the point S 18 19 20 21 22 29 28 According to the theorem AS BS CS DS Use the Cabri II built in calculator to verify this result Select Calculate from the Measure toolbox ninth button A calculator appears at the bottom of the screen Move the toward the measurement of AS until the message This number appears Click once to include the measurement in the calculation A marquee box appears around the measurement along with an a The variable a also appears in the calculator edit window Now click on the multiplication button Next select the measurement of BS To complete the calculation click on the equals button The result is displayed in the calculator result window Move the result into the drawing window by clicking once on the result window An empty marquee box appears in the drawing window Move the 8 pencil to move the box to a location near the measurements Click to place the result The calculation is tagged with the label Result Select the Comments tool from the Display toolbox Move the cursor toward the label Result until the I I beam and the message Edit this text appear Click once to open an edit window around the label and the measurement Highlight the label by dragging the cursor across the text and then enter a new label AS BS Repeat steps 18 22 for CS a
37. ints the 8 5 by 11 0 inches 21 59 by 21 94 cm drawing area Copying permitted provided TI copyright notice is included Getting Started with Cabri Geometry Il 3 1997 1999 Texas Instruments Incorporated 4 Getting Started with Cabri Geometry Il Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated Getting the Most from Getting Started About the Getting Started Guide The Getting Started guide introduces you to Cabri Geometry II with hands on exercises However it does not cover all features of Cabri II nor does it demonstrate all the ways to construct any particular object Getting Started includes the following sections First Steps This section provides system requirements and installation instructions for Cabri Geometry II and briefly discusses the Cabri Geometry II tools Checking System Requirements Describes requirements for Windows DOS and Ma cmtosh systems 2 552 eet ek ERE Rab IU E eet eho eo bat Rein eae Sk BE 6 Installing Cabri Geometry Il Explains how to install Cabri Geometry II 6 Starting Cabri Geometry Il Explains how to start Cabri Geometry II 7 Cabri Geometry Il Desktop Briefly describes the Cabri Geometry II screen and toolbar 8 Quick Reference Sheet Gives a list of the tools under each toolbox in the Cabri Geometry IElOOIDAT 2282 D UC bei per acta ot de qr eee o WEEE SLES GRO Res 9 Basic Operations
38. is included Getting Started with Cabri Geometry l 43 1997 1999 Texas Instruments Incorporated Toolbar Commands Continued _ Light lines Thick lines mee 0000 Small point Medium point Large point T Crosspoint Cross 44 Getting Started with Cabri Geometry Il ER 7 n k 1 tick mark 2 tick marks 3 tick marks HE Cartesian coordinates Polar coordinates measured in degrees Polar coordinates measured in grads Polar coordinates measured in radians m Colored background m In colored box Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated
39. ith the factor 1 2 Select the Numerical Edit tool from the Display toolbox tenth button if necessary Click at the location where you would like to place the numerical value you can place it anywhere in the quadrant A numerical edit window appears 35 Type the value 1 2 in the numerical edit window Then press U Macintosh or CTRL U Windows DOS to see the list of units Select the option Without unit No unit is assigned to the value Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated Getting Started with Cabri Geometry Il 23 Exploring Transformations in the Coordinate Plane Continued Dilate the polygon by a defined factor continued 36 37 Select the Dilation tool from the Transform toolbox sixth button Move the toward the original polygon until the message Dilate this polygon appears Click to select the polygon Move the toward the origin point until the message with respect to this point appears Click to select the point Now move the toward the value 1 2 until the message using this factor appears Click to select the value An image of the polygon that is dilated by the factor 1 2 with respect to the origin point is created Dynamically change the dilation factor 30 39 Select the Numerical Edit tool from the Display toolbox tenth button Move the I I beam cursor toward the value 1 2 until the message This number
40. nd DS Change the label on the result to CS DS Getting Started with Cabri Geometry II amp 5 5 29 cm ES 1 21 em CS 2 58 cem D5 1 16 cm OFF Cancer e Inv SIN EOS TAN CL E t Result 3 93 cm a5 325 cm BS 1 21 em AS BS z 9z om CS 3 38 cm D5 1 156 cm ES DpS z 9z om Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated Manipulate the construction to explore the results 24 Select the Pointer tool from the Pointer toolbox Evaluate the proposed theorem by manipulating the construction As you drag point or point C around the circle does the property hold true That is do AS BS and CS DS remain constant 25 Drag point S to a new location within the circle What happens to the calculation results Now drag point A and point C around as before Does the property still hold true 26 Drag point to several locations within the circle while monitoring the power of the point calculations Make a list of your observations A partial list of observations is shown at the end of this exercise Construct a table 27 Construct a table of values to support your generalizations Select the Tabulate tool from the Measure toolbox ninth button To define the size and location of your table move the pointer to an unoccupied location in the drawing window Press and hold the mouse button down Move the cursor to another location to
41. o create a new point inadvertently refer to the steps in the Checkpoint 1 box to delete it 20 Repeat step 19 to create line segments to model all possible handshakes Copying permitted provided TI copyright notice is included Getting Started with Cabri Geometry l 15 1997 1999 Texas Instruments Incorporated Modeling Handshakes Continued Count and record the handshakes 21 To keep track of each handshake as you count it use the selection feature Click on the first line and then press and hold SHIFT as you click on each additional line The change in appearance of each line helps you keep track as you count Enter the number in the chart at the beginning of the exercise Click outside the circle to deselect the lines Open the on screen attribute palette 22 You can help differentiate new points and handshakes from the old points and handshakes by using the color point and E line attributes ol mi mj m For convenience you can create a customized on screen mi ol mi mi mi attribute palette of the attribute icons m mJ mi mi Click and hold on the Color Attribute toolbox the top button PIN on the attribute toolbar however instead of selecting a color when the palette opens hold down the mouse button and drag the entire palette onto the drawing window Release the mouse button Click on each of the attribute buttons on the vertical attribute toolbar to add the tools to the on screen attribute palette
42. objects interactively Jean Marie Laborde and Franck Bellemain developed Cabri Geometry II at the Institut d Informatique et Math matiques Appliqu es de Grenoble IMAG a research lab at the Universit Joseph Fourier in Grenoble France in cooperation with the Centre National de la Recherche Scientifique CNRS and Texas Instruments Texas Instruments the publisher for Cabri Geometry II in the United States and Canada is pleased to bring computer based geometry to classrooms The geometric foundation of this easy to use software encourages exploring and 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 Discretes et de Didactique LSD2 a research laboratory within IMAG He graduated in mathematics at Ecole Normale Sup rieure in Paris in 1969 He earned a Ph D Th se d Etat in computer science at the University of Grenoble in 1977 Jean Marie began work on the Cabri II project in 1981 as an environment for graph theory He has devoted his research efforts to the use of geometric methods for the study of different classes of graphs especially hypercubes Franck Bellemain earned a Ph D in mathematics at the Universit Joseph Fourier in 1992 He began work on the Cabri IT project in 1986 and is responsible for writing several versions of the software for Macintosh PC compatible and Japanese computers His
43. ons circles and other basic objects e Translates dilates and rotates geometric objects around geometric centers or specified points plus reflection symmetry and inverse of the objects e Constructs conics easily including ellipses and hyperbolas e Explores advanced concepts in projective and hyperbolic geometry e Annotates and measures figures with automatic updating e Uses both Cartesian and polar coordinates e Provides for user display of the equations of geometric objects including lines circles ellipses and coordinates of points e Allows the user to create macros for frequently repeated constructions e Lets the teacher configure tool menus to focus student activities e Checks geometric properties to test hypotheses based on Euclid s five postulates e Hides objects used in constructions to reduce screen clutter e Differentiates objects through the use of paint like color and line palettes e Computes a locus continuously e Illustrates the dynamic characteristics of figures through animation e Allows the user to save drawings and macros to disk e Opens geometry constructions created on the TI 92 e Provides one square meter of full size work space and prints the 8 5 by 11 0 inches 21 59 by 21 94 cm drawing area Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated About Cabri Geometry Il Cabri Geometry II lets you construct and explore geometric
44. otate a polygon by an angular value that you Se LEE define This example begins with the value 30 First remove the polygons created previously To do this select the Pointer tool from the Pointer toolbox first button Then press and hold the mouse button in a blank area outside the polygons and vector Drag the mouse across the drawing until a marquee rectangle surrounds all of the objects Release the mouse button All of the objects in the rectangle are selected except the axes which cannot be removed in this manner Press DELETE on your keyboard The objects are removed 27 Select the Polygon tool from the Lines toolbox third button y Construct a four sided polygon in the upper right quadrant Make it any shape you want 28 Select the Numerical Edit tool from the Display toolbox tenth button Click at the location where you would like to place the numerical value you can place it anywhere in the quadrant numerical edit window appears 29 Type the value 30 in the numerical edit window Then press without unit U Macintosh or CTRL U Windows DOS A list of units HEC appears in a pop up menu PRESSE Meter Select the unit Degree The degree symbol is assigned to Kilometer the value 30 Square Millimeter Square Meter Radian Degree k Grad 1997 1999 Texas Instruments Incorporated 30 Select the Rotation tool from the Transform toolbox sixth button
45. ows DOS Overwrite the default name New construction and enter the name Segment Division from your keyboard in the field labeled Name of the construction It is not necessary to save the macro to a file in this case since it is an intermediate step in the construction of the pentagonal curve of pursuit However if you wish to save the macro to a unique file on disk click on the Save to file box to mark it J with an x This is your only opportunity to save the macro to an independent file although it will be senate saved automatically with the construction Note Colors available in Windows version only Copying permitted provided TI copyright notice is included Getting Started with Cabri Geometry l 33 1997 1999 Texas Instruments Incorporated Constructing a Macro Pentagonal Curve of Pursuit Continued Note It is not necessary to save a macro to disk to use the macro If you save the file the macro also will be saved with the file provided it was used in the construction 9 Click on OK to save the macro 10 The macro now appears in the Macro toolbox with the name St told sil ml Segment Division This macro will generate a point that is ETTA located on a segment at one eighth of its length Etil Ubject Deine erre Note Macros created using a segment as the initial object segment buisinnk can also be applied to the side of a triangle polygon or regular polygon Test the
46. points created by the si i Segment Division macro now are being used in the definition of the new macro Copying permitted provided TI copyright notice is included Getting Started with Cabri Geometry l 35 1997 1999 Texas Instruments Incorporated Constructing a Macro Pentagonal Curve of Pursuit Continued 18 19 20 21 22 23 36 Select Final Object from the Macro toolbox Select the inner pentagon as the final object The macro is now ready to be defined Note A macro generates its final object with the object s existing attributes when Define Macro is chosen These attributes can be changed at any time prior to the selection of Define Macro Select Hide Show from the Draw toolbox last button Select each vertex of the final object the inner regular pentagon These points will be hidden when the regular pentagon is generated from the macro Select Define Macro from the Macro toolbox A dialogue box appears in which you name your macro Enter the name Pentagram from your keyboard in the field labeled Name of the construction Click on the Save to file box This is the only opportunity to save the macro to an independent file although it will automatically be saved with the construction You can enter a help message and the name of the first final object for future reference It is a good idea to document how your macro works in these fields Enter appropriate messages
47. rated First Steps Continued About Cabri Geometry Il Tools In Cabri Geometry II you use one construction tool at a time The tools are displayed as groups of buttons on the toolbar across the top of the screen The buttons often called toolboxes are referenced from left to right in the text Cabri Geometry Il Screen The screen shown below illustrates the Macintosh version Screens on Windows and DOS systems are similar but slightly different Help Icon Toolbar Menu Bar 2i adel A Az Close En 7 Figure Zoom Box E Er Box a 4 ei m m A mj m m m mj sj mE E Jn Attribute Attribute l PRENE Icons B Drawing Window n Size m 0 5 5 J 2 N VN ij Zu Box penam OA Pointer Message Scroll Bars Help Window Selection Pointer Cabri Geometry Il Toolbar Pointer Points Lines Curves Construct Transform Macro XJ JO A x Check Property Measure Display Draw 1997 1999 Texas Instruments Incorporated QUICK REFERENCE SHEET CABRI GEOMETRY Il m 07 1 21 18 10 0 B7 1 US a QR S L O g SU o e S g S u o eos il SS SNO Q d S o O Q9 JS gf FPF WM X45 SM 9 E i i CONSTRUCT DE Perpendicular Line Parallel Line N Dilate Lan HT A pa POINTER Pointer faa a z m JJ O D D Midpoint Rotate and Dilate Perpendicular Bisector POINTS Fa ul Fa Angle Bisec
48. reated and release the mouse to select it Your computer s response will become slower as more objects are added to the construction Optional macros It is also possible to combine more steps in a macro For example create four inscribed pentagons select the original pentagon as the initial object select the remaining pentagons as the final objects The macro then will generate four inscribed pentagons Other line designs Try using this technique to construct other line designs This example was inspired by Dale Seymour s book Introduction to Line Designs published by Dale Seymour Publications Copying permitted provided TI copyright notice is included Getting Started with Cabri Geometry II 1997 1999 Texas Instruments Incorporated 37 Menu Options Ctrl N New 0 Open a new Cabri Geometry II drawing Ctrl O Open Open a saved Cabri Geometry II drawing Ctrl S Save Save the current Cabri Geometry II drawing in the file from which it was loaded fSaveas O save the current Cabri Geometry II drawing to a specified file Revert Replace the current drawing with the most recently saved version Ctrl P Show Drawing Zoom out to the one square meter drawing sheet reposition the window Page Setup Select printer and page options Macintosh Windows Printer Setup DOS Print the current page Macintosh Windows DOS or the entire drawing area Macintosh only Ctrl Q Quit 0 Close Cabri Geometry II
49. step instructions are given below Follow the steps and fill in the chart at the right Do you see a pattern Get ready 1 Start Cabri Geometry Geometry IL Click anywhere in the drawing window to remove the initial screen The drawing window appears Construct a circle to represent the party 2 The fourth button on the toolbar represents the currently selected tool in the Curves toolbox The toolboxes have been assigned names for convenience the names do not appear on the screen Click and hold on that tool to pull down the menu of tools used to construct curved lines 3 Point to and click on the Circle The circle tool is displayed in the toolbox Notice that this button is lighter than the others and has the appearance of a button that is pushed in This tells you that Circle is the currently selected tool 4 Move the pointer toward the center of the drawing window As you move the onto the drawing window it changes to a 8 pencil so that you can draw a circle Click and release the mouse button A dot appears 5 Move the away from the point Do not hold the mouse button down As you move the 9 a circle appears Continue to move the 9 to change the size of the circle When the radius of the circle is about two or three inches click again Notice that the Circle tool is still highlighted indicating that you can make another circle immediately without having to select from the toolbar again Copying
50. t must select initial object s that are used to define the final object s The next step is to select the final object s and then if necessary to change the attributes of the object s as they will appear in the final construction The final step is to define the macro for inclusion in the Macro toolbox The macro is then available for use Select the segment as the initial object 5 Select Initial Object from the Macro toolbox seventh button Move the toward the segment until the message This segment appears Click to select the segment as the initial object The segment appears to be moving or flashing a marquee outline indicating that it is selected Select the point that is one eighth the length of the segment as the final object 6 Select Final Object from the Macro toolbox Move the xls this point toward the second point from the right on the segment until the message This point appears Click to select this point as the final object The point flashes 7 You are now ready to define the macro Select the Define Macro tool from the Macro toolbox A dialogue box appears in which you can name your macro 8 Macintosh Enter the name Segment Division from Macintosh the keyboard in the field Name of the construction Es Notice that the letter in the icon font field changes c prm rt to S This letter will appear as an icon in the Macro toolbox identifying the Segment Division macro Cancel Wind
51. th button Move the 9 toward the segment until the and the message Midpoint of this segment appear Click once The midpoint of the segment appears The segment is divided into halves 4 To divide the segment into eighths you need to divide the segment into two more halves That is 1 2 1 2 1 2 1 8 Use the Midpoint tool to perform the division Move the 8 toward the midpoint until the 5 and the message Midpoint between this point appear Click once Move the toward the end point on the right until the 4 and the message and this point appear Click once The midpoint between the two selected points appears The segment has a one quarter division Divide the right most quarter again using the Midpoint tool The segment now has a one eighth division 32 Getting Started with Cabri Geometry Il Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated Define a macro to perform a segment division To build a pentagonal curve of pursuit you need to find a point on each side of a regular pentagon that is one eighth the distance of that side The segment division performed in the previous steps shows the procedure you need to accomplish the task Macros are used to perform repetitive tasks or to create unique objects Since building a pentagonal curve of pursuit is a repetitive task it would be beneficial to create a macro that would perform the task To create a macro you firs
52. tor Vector Sum U o 2 RAT Al A Point on Object Compass 2 1 Intersection Point Measurement Transfer A uf Locus bal a Line 4 Redefine Object mM Segment ae S Ray Translation id Rotation Dilation Heflection OR z Regular Polygon Symmetry E Circle Arc LE Initial Object ni Si Final Object hen Define Macro Inverse SO Conic Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated Getting Started with Cabri Geometry II CHECK PROPERTY Oollinear Parallel Perpendicular Equidistant Member Distance and Length Area Slope Angle Equation and Coordinates Calculate Tabulate DISPLAY Label Comments Numerical Edit Mark Angle Fix Free Trace On Off Animation Multiple Animation DRAW Hide Show Color Fill Thick Dotted Modify Appearance Show Hide Axes New Axes Define Grid 9 1997 1999 Texas Instruments Incorporated Modeling Handshakes wants to shake hands with the others How many Problem Four friends meet at a party Each New handshakes Total handshakes handshakes take place A fifth friend enters the room then a sixth and seventh How many handshakes are there You can use Cabri Geometry II to model this situation by constructing points on a circle to represent the friends and line segments to represent the handshakes Step by
53. tration for each version Therefore some illustrations in this guidebook may be slightly different on your computer Copying permitted provided TI copyright notice is included Getting Started with Cabri Geometry I 5 1997 1999 Texas Instruments Incorporated First Steps Checking system requirements Macintosh Macintosh Classic or better System 6 0 or later 1 Mb available RAM for a Macintosh Classic Memory requirements will be greater for color or larger monitors than on the Classic Hard disk with 1 2 Mb available for program and demonstration files Windows 3 1 386 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 Installing Cabri Geometry Il Macintosh 1 Create a folder named Cabri Il on your hard disk Insert the Cabri Geometry IT Macintosh diskette in your floppy disk drive Double click on the Installer on the diskette and follow the directions on the screen Windows 3 1 1 Insert the Cabri Geometry II 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 Installing Cabri Geometry Il on a network DOS DOS comp
54. utton and add the coordinates to the reflected triangle Select the Pointer tool from the Pointer toolbox first button and try to drag the new triangle What happens Try to drag the original triangle What happens The reflected triangle is dependent upon the original triangle and cannot be moved independently Select the Symmetry tool from the Transform toolbox sixth button Point to and click on the triangle in the upper left quadrant when the message Reflect this triangle appears Then click on the point at the origin when the message with respect to this object appears A triangle that is symmetric to the origin appears in the lower right quadrant Add the coordinates to the reflected triangle with the Equation amp Coordinates tool from the Measure toolbox ninth button Select the Pointer tool from the Pointer toolbox first button and drag the triangle in the upper right quadrant into each of the other quadrants Getting Started with Cabri Geometry Il 0 432 cm 2 67 2 28 3 34 2 08 1 54 1 32 1 055 em 2 77 2 61 3 81 2 25 1 16 1 12 Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated Construct a polygon 19 Open a new drawing by selecting New from the File menu 20 Display the coordinate system by selecting the Show Axes tool from the Draw toolbox last button 21 Select the Polygon tool from the Lines
55. weight Add the new handshakes Remember to click only when the message says This point so that you don t create a new point Count the handshakes and enter the results on the chart at the beginning of the exercise Add the sixth and seventh friends and handshakes 26 Add the additional friends and the associated handshakes Change the line color and attribute for each Count the handshakes and complete the chart Do you see a pattern Can you predict how many handshakes there are for eight friends For 20 friends Generalize the equation Solution The total handshakes are 6 10 15 and 21 requiring 4 5 and 6 new handshakes for the fifth sixth and seventh friends respectively In general the number of new handshakes required is n 1 and the total number of handshakes is n n 1 2 Copying permitted provided TI copyright notice is included Getting Started with Cabri Geometry II 17 1997 1999 Texas Instruments Incorporated Exploring Transformations in the Coordinate Plane Problem What happens to the Coordinate values of a triangle that is constructed vn the upper right quadrant and then trans formed in various ways Explore using Cabri Geometry II to find out Get ready 1 Start the software see page 1 3 if necessary or select the New option from the File menu if the drawing window is A already displayed You will be prompted to save your current construction if one exists Display the r
56. which contains the numbers in sequential order Each number represents a row The entire row appears in gray Press the DELETE key to delete the values in that row The remaining values move up one row 33 Point to the first row of a column and click The first row is the row which contains the title of the column The entire column appears in gray Press the DELETE key to delete the values in the column The remaining columns move left Repeat to delete the values in the remaining columns Animate the construction 34 Animate the construction to record data in the table automatically Select the Animation tool from the Display toolbox Next move the until the message This table appears to select the table The table is enclosed in a marquee rectangle to indicated it is selected 35 Move the pointer to point A until the message This point appears Press and hold the mouse button and move away from the point The animation spring is connected to the point and the cursor Release the mouse button to start the animation The animation spring indicates the direction and relative velocity of the animation Click again to stop the animation Values are recorded in the table automatically There are many facets to this problem We encourage you to explore further Copying permitted provided TI copyright notice is included 1997 1999 Texas Instruments Incorporated wee TELLLLLLLLLLLLEEEEEEEEEEEEEEEESEEE OEEEEREREEEEER
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