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1. Truncated Cube Yves Martin IV 1 Main Menus 1 File Menu pe 1 BE New Ctrl N New Open a new drawing sheet Ctrl O 0 Opn Open an existing drawing sheet Ctrl S Save the current Cabri drawing Save As Save the current drawing under a name to be specified Restore Restore the most recently saved version Ctrl P Show Page Show the full drawing page 1 m2 This enables work to be repositioned within the page a Page Setup Definition of parameters for printing Print Print the current area or the full page on Macintosh only Ctri Q Exit Quit Cabri Geometry 26 2 Edit Menu et A Ctrl X Ex eat ora a Remove the current selection to the clipboard Ctrl C Copy the current selection to the clipboard Ctrl V Paste clipboard contents to current drawing Ctrl A Select All Select all the objects in the drawing Replay Construction Enables the construction to be replayed There are several possible options Ctrl F Refresh Drawing Delete all trace lines from the drawing trace option Figure 1 The list of open drawings is shown in this menu Macintosh only In Windows see the Windows menu 3 Options Menu Show Attributes Display or hide the toolbar which controls the appearance of objects Petes ete io acon thickness marks etc Macintosh only Preferences 000 Choose the settings for locus axes units precision equations __ Toot configuration Selection2. VII 1 Windows Version The available printers are listed in the window which s displayed when the Printer button in the Page setup is clicked or when Print is selected both from the File menu This dialog box allows various settings related to printing to be changed Page Setup 71x Page Setup 21x Printer Name EPSON Stylus Photo 700 gt Properties Status Default printer Ready Type EPSON Stylus Photo 700 Where LPT1 Comment Paper Size 44210 x 297 mm M Source Auto Sheet Feeder Orientation r Margins millimeters Portrait Left 25mm Right 25mm C Landscape Top 25mm Bottom 25mm Cancel Printer The printer drivers are those installed with the system 47 Exporting diagrams to other software A diagram can be copied by selecting an area of the screen using the pointer tool k then using the Edit menu The copy is held on the Windows clipboard so that it can be pasted into a word processing package such as Word or a drawing package such as PaintBrush In Preferences a choice can be made between a Bitmap or vector image The quality of the results depends on the particular word processing package being used the later ones such as Word 97 give better results VII 2 Macintosh version Only The creation of documents to be printed or exported to other software such as Word or MacDraw require the application of some extra techniques to get the best appeara
3. Display the axes and mark a point M on the x axis Display its coordinates Enter two numbers a and b using Numerical Edit from the Display toolbox Open the calculator Calculate from Measures Use the mouse to select the number a on the screen which will then be displayed on the calculator Next multiply the number by sin b c b is similarly selected by clicking on it and c is the x coordinate of M Confirm the formula by pressing Enter or by clicking on Ire SIN Cos TAN ILA LN Loci ABS m LOL 24 With the mouse click on the calculated value and drag it to the drawing area Use Measurement Transfer from the Constructions toolbox to transfer this number to the y axis Click on the value then the y axis Construct point P x y where x is the abscissa of M and y 1s the calculated value Call up the locus of the point P as x moves along the x axis The number of points in the locus could be increased or x could be limited to an interval to improve the display Change a and b to see the effect of these parameters You can also change the formula PC use the Pointer tool to click on the number and type Ctrl R or Mac double click on the number and bring up the CALC menu Change sin into cos confirm and observe the changes in the graph y Result 1 44 Try with b 2 0 other functions 9 3 0 A 0000 25 IV Cabri Geometry II Keyboard and Menu Functions
4. CABRI GB IR YU USER MANUAL mm UNIVERSITE CABRILOG ese Os Cabri Geometry II also known as Cabri G ometre II was developed at IMAG the department of Information Technology and Applied Mathematics Universit Joseph Fourier Grenoble and CNRS the National Centre for Scientific Research France The company CabriLog S A S is henceforth responsible for the development support and commercialisation of Cabri Geometry This software package is the result of work by a team of mathematicians educators and computer specialists led by Jean Marie LABORDE It has received support from the Office for New Technology in Teaching at the Ministry of National Education in Paris and 1s officially recognised as being of educational value The Windows version has been distributed in France since 1997 by the Ministry of Education The TI 89 TI 92 and the new Voyage 200 PLT calculators from Texas Instruments incorporate Cabri Geometry II to provide its geometrical facilities This guide will enable you to start working with Cabri Geometry II The versions for Windows MS DOS and Macintosh are very similar the few differences are mainly in file handling copying printing multiple windows etc The files can be transferred between operating systems without modification They are text files which can be easily loaded into a word processing package Active Geometry files and activities for Cabri are available from the UK Cabr
5. With calculator the key has the same function as equals that is to say it evaluates the expression and on the Macintosh the a key enables the result to be transferred to the drawing area However it must still be positioned correctly using the mouse and clicked to fix it These keys start a multiple animation after the springs have been put in position e The key enters an extra line in text Backspace Deletes the selected object To delete all objects n the drawing area first Select All with jer fa or LG A then press Backspace For text and numbers it deletes the character to the left of the cursor If a number in the middle of text 1s selected it deletes the number e During a construction the last action creation or selection is cancelled without quitting the current tool 45 Delete jan On the PC only the Delete key operates in the same way as Backspace to delete a selected object to delete all objects to cancel the last action in a construction but with the usual proviso in text or numbers it deletes the character to the right of the cursor in other words it deletes in the direction in which one writes from left to right while Backspace removes a mistyped character and deletes from right to left ri El On the PC this opens the help window to get a description of the tools 46 VII Editing and Printing Diagrams Parallels and Meridians on the Pseudosphere Yves Martin
6. and these preferences can be saved to disk For a locus the number of points used to create it affects its appearance on the screen and also the speed of any changes to it You can change the number of points for each locus directly by selecting the locus and using the i or keys or by changing the preference settings You can also obta n envelopes of straight lines or the complete set of straight lines according to the choices made after selecting the Loci Options tab in the Preferences w ndow For the colour of objects some printers will not print all colours By carrying out test prints you will be able to adjust the preferences so that certain objects are not invisible in a printout because of an unsuitable choice of colour 36 Preferences 2Ix Display Precision and Units Coordinate System and Equations Loci ptions Default Styles Geometry System Options Number of objects in locus e Locus of points IV Link points Locus of lines Iv Envelope Selecti Factory Settings Apply to z oe Keep as defaults Save to file Close Windows Preferences showing different levels of choice The System Options tab contains an option to use bitmap images The default setting 1s for bitmap For a better quality printout cancel this selection before copying and pasting into a word processing package 2 On a Macintosh Preferences Window 7 Loci options Number of objects in locus 5
7. marked tL Select Line from the Lines toolbox then one vertex and its opposite midpoint for each median to be constructed A Mark the centroid at the intersection of the medians Label it G 5 Other constructions e Construct the centre of the circumscribed circle at the intersection of the perpendicular bisectors of the sides e Draw the circumscribed circle e Construct the centre of the inscribed circle at the intersection of the bisectors of the angles e Draw the inscribed circle 14 6 Appearance of the diagram The diagram is becoming complex so to improve its appearance either hide parts of the construction using the 2 icon when an object is selected its outline becomes dotted and it will be hidden To redisplay the hidden object just select it when the 2 tool is active or by using dotted lines thicker lines or colour The available tools are Hide show Hides shows the objects in the diagram Enables polygons circles and text to be filled gj o Enables line thickness to be changed Dotted Enables line style to be changed x Modify appearance Enables certain attributes of objects to be changed shape of points angle mark segment mark reference system text style li Wo Enables the colour of an object to be changed See Chapter IV for other ways to change the attr butes of the various objects 7 Construction macros It can be useful to save the construction of the circumscr
8. number 1000 Locus of points X Link points Locus of lines X Envelope Displayed Precision Equation Formats 1 Angle 1 decimal Circles x a y b R2 Conics au buyscy diseyf 0 C Save to file and Selection Factory Settings Applyto ix New objects 37 V 2 Default Setting Macintosh only The Defaults item from the Options menu enables the colour and certain attr butes of objects to be chosen such as line thickness point symbol etc Cabr II will save these settings to disk in the preferences file Help Show Attributes Defaults Preferences Tool Configuration Language Font Size Style b gt gt gt Defaults Window Attribute Settings Points Thikness 2 Lines Small Dots Polygons Large Dots Vectors Point Type Circles Conics Angle Marks Be Loci Text T Axes Grids x Implicitely defined points Arcs x Objects at infinity Save to file and X Selection Apply to X New Objects V 3 Configuring the Tools As in version 1 Cabri II can be configured with customised tools This can be particularly useful to modify the package for younger pupils or to create particular problem situations It s also very convenient in particular types of work vectors conics hyperbolic geometry where sets of macros
9. The names of the tools used at each stage of the construction appear in the Replay construction window reached via the Edit menu The appearance of this window in the Windows version 1s shown in the diagram below Replay Construction Trianale amp B Cflast constructed object OK Cancel Replay construction window Windows version The and buttons are used to advance and retreat through the stages of the construction The K and buttons jump straight to the beginning or end of the construction n When quitting this window the construction replay picks up from where it was previously A dialog box gives the choice of whether or not to return to the completed figure On the Macintosh TE Ei kK ol dj lt m p ro e vi Go to the first step of the construction Go to the last step of the construction Stop only in the replay of a loop operation Replay the construction step by step forwards or backwards Fast forward or return 10 steps Pause ls BIE lm e als Automatic replay the direction must also be chosen When quitting this window the construction replay picks up from where it was previously A dialogue box gives the choice of whether or not to return to the completed figure The names of the tools used do not appear in the Macintosh and DOS versions 40 41 VI Shortcuts Cabri Geometry has several shortcuts which are accessed mainly via the keyboard but also us
10. can be grouped so that they are opened together Select Tool Configuration from the Options menu It is possible to enter a password to prevent unauthorised access to menu modification 38 Tool Configuration Select and move items you want to change Password optional O up to 8 characters Save to file When the dialog box is opened a waste basket appears at the righthand end of the tool bar Tools are removed by dragging them to the waste basket x HO Aa sl dd nj Individual tools can be placed on the tool bar or the contents of toolboxes can be changed by moving a tool from one box to another This 1s a simple example of a paper and pencil tool bar created with Tool Configuration Y HA Se 2424 Al It could for example be used at Key Stage 3 but also with other classes according to the activity to be undertaken This second example is a tool box which could be used at A level Vector Display as vector Vector sum Vector difference Components of a vector Multiplication of a vector Scalar product Linear combination 2 vectors Encouraging students to create their own tools for later use is a very instructive activity 39 V 4 Replay Construction Replay construction from the Edit menu enables the stages of a construction to be reviewed step by step By first selecting the zx icon one can also see the objects that have been hidden during a construction Windows version
11. of the construction Name for first final object Help for this macro Tvpe in some text The appearance of the dialog box in the Macintosh version This is the dialog box for Windows On a Macintosh the appearance of dialog boxes is slightly different but the overall operation is the same 16 After validating your macro with OK it becomes available in the Construction Macros toolbox Its icon carries the initial letter of the name you have chosen or the icon that you have designed If you save the macro to disk you will in a dialog box be able to change or keep the name of the saved file before clicking OK No more than 8 characters on a PC running under DOS or Windows 3 Cabr II enables you to change the initial objects in your macro and to obtain the same final object from the same macro To do this start a new macro with the three vertices of the triangle as initial objects then select the centroid as the final object image Confirm the macro as before giving it exactly the same name You will get the following message Augment or replace a macro definition A macro construction with the same name already exists Do you want to augment its definition or replace it Replace Cancel Dialog box Windows version By clicking OK you will have obtained one single macro with two possible choices for its initial objects the triangle or its three vertices In the Windows version th
12. pi Pi CEIL value ceil Ceil FLOOR value floor Floor IO value SORT value sqrt Sqrt SqRt V S gne SIGNE sign returns 1 0 1 SIN value sin Sin SINH value sinh SinH sh TAN value tan Tan TANH value tanh TanH th ABS value abs Abs 34 IV 4 Attributes Toolbar This toolbar 1s accessed from the Options Menu The attributes toolbar is deployed to the left of the screen and can be extended into several palettes which enable the various attributes to be selected for the objects in the diagram These tools enable you to check the appearance of the objects that you are going to create For example to choose the colour for circles select the circle tool on the icon bar then choose the colour from the palette in the toolbar From this point all the circles will be of this colour An object or a group of objects can have their appearance modified by using the toolbar It is often preferable for printing in black and white to select all the diagram and then choose black from the colour palette This ensures that the print out has sufficient contrast as greens and light blues are often difficult to see when printed The same tools can be found in the Draw toolbox However these latter tools work differently For example if Colour is selected from this toolbox you get the colour palette and you select first the colour then the objects to be coloured The
13. point move the pointer until the message This point 1s displayed then click and drag the mouse 2 Translation You can also move the pointer towards the side of the triangle and when you see This triangle displayed you can move the whole triangle by clicking and dragging the mouse This move is a translation it s the reason why we label the pointer k Translation Pointer Other pointers You can select other pointers from the Pointers toolbox to rotate and or enlarge the tr angle Li Pointer Rotate Dilate Rotate and Dilate The default centre for rotation or enlargement is the geometrical centre of the figure You can click on a point previously created with the Point tool which you wish to designate as a centre before making the rotation or enlargement 12 3 Construction of altitudes and the orthocentre To construct the alt tudes select the Perpendicular Line tool from the Constructions toolbox x JAC Bede te 242 Select a vertex then its opposite side to construct an altitude Do the same for the other two altitudes The foot of each altitude 1s designated by selecting the menu item Point from the Points toolbox Mark a point at the intersection of the side and the altitude Cabri Geometry II displays the message Point at this intersection which shows that it will construct the point as a point of intersection In Cabri g ometre I you ve had to choose the menu item Intersecti
14. the printer with a black and white printer patterns are used instead of fill colours If your document s to be photocopied you can select the black and white option for printing whatever the type of printer 1n the Printer Driver dialog box With a PostScript printer it is obvious that the drawing will benefit from the extra precision available Colour Grey Tones If colours are rendered by grey tones the spacing of the dots used can give a dotted appearance to plain coloured lines Darker colours give better results for printed 1mages It 1s possible for a line to fall into the blank section of the matrix of dots so that it disappears when printed This happens particularly to pale green horizontal lines Extra fine Lines With PostScript printers it is possible to get extra fine lines by holding down the Alt or Option key when clicking on OK in the Print dialog box This option only affects the thickness of fine lines Print options The options are available in the dialog boxes e Page Setup paper size enlargement reduction portrait landscape e Print number of copies colour black and white name of author name of drawing date Changing these options when there 1s no drawing open or while the working area has still not been saved deals with the default Print settings for Cabri II 1 e the original settings when opening Cabri II or at the start of a new drawing When a drawing is saved the settings us
15. 1l Translation Construct a regular pentagon use Regular polygon in the Line toolbox Construct a vector AB Construct the image of the pentagon under translation by the vector AB By reading the cursor messages carefully you can resolve many of the difficulties that arise due to the order of operations Translation from the Transformations toolbox Move points A and B then the pentagon See page 29 for the description of this tool 20 2 Rotation To define a rotation an angle must be included This angle can come from the diagram or the numerical value can be entered seperately Enter a number using Numerical Edit from the Display toolbox select Numerical Edit then click on the drawing where the number is to be displayed type in a number eg 30 and select the units degrees by choosing this from the small menu labelled U on the Macintosh On the PC the boxes for entering numbers and text do not have pop up menus The menu for choosing units 1s opened by the short cut Lv from the keyboard TE Without Unit Millimetre Mark a point O which will be the centre of Centimetre rotation Next select Rotation from the etre Transformations toolbox aes 1 Square Millimetre To rotate the pentagon through 30 about O Square Centimetre click successively on the polygon the angle Square Metre and the centre The order can be changed Square Kilometre for certain elements just follow the c
16. ancel 42 Tabulation s with axes selected changes from cartes an to polar coordinates and loops successively through degrees grades and radians then back to cartesian zi with equation selected changes the type of equation straight line circle or conic if that Is possible a in table adds a line of values selected from the table Plus and Minus L1 f e When a number is selected these keys add to or reduce the number of decimal places displayed e They increase or decrease speed during an animation e They increase or decrease the number of points in a selected locus Shift Lel Standard selection Enables several object to be selected and increases or decreases a multiple selection Special selections In a certain number of special modes Trace Hide Show Fix Free Initial objects or Final objects in macros selection operates as if it were Shift selection in standard mode and the shift key then allows everything to be deselected by clicking in the page For example for Show All just select Hide Show then click in the page while holding down the Shift key Snap to changes e Holding down the Shift key restricts certain moves or positioning e For straight lines segments axes etc rotation in steps of 15 when moving or creating objects e For circles regular polygons once created and axes the extension or reduction of a ray or spacing of a scale mark by whole cent
17. and arrangement of tools Language Language selection O BEEN Font Macintosh Font selection Size Macintosh Selection of character s ze Style Macintosh Application of a Application ofa style Font Windows be eal three Macintosh items above are selected in a dialog box instead 4 Window Menu Windows only Cascade Standard Windows menu for managing open files Tile Horizontally and the display of the open windows Tile Vertically Close All Figure 1 The list of open drawings is shown in this menu 27 IV 2 The Toolbar The toolbar contains a row of icons Pointers Points Lines Curves T Constructions AAO 2d eel a a Transformations _ Macros Chec k Properties Measures Display Draw Each icon corresponds to a word or phrase which describes the appropriate object This is fundamental for teaching geometry to children who manipulate objects and learn the terminology at the same time thus enabling them to talk about the geometry they are doing Line Line Segment Segment Ray Ray Vector Vector ts Polygon Polygon Regular Polygon Regular Polygon Triangle Triangle _Polygon _ Polygon Click and Hold hold down the lefthand mouse button when pointing at an icon to open a toolbox a list of tools appears The icon of the chosen tool then replaces the original one on the toolbar A quick single clic
18. ation 1s then displayed and can be edited The change in a calculation 1s immediately updated in the diagram In Windows the calculation can also be displayed by a single click on the result in the drawing then typing CTRL R There are other functions available on the calculator than those which are listed on the screen Given below s the list of functions and their syntax Functions available from the calculator Function Arc Cosine Hyperbolic Arc Cosine Arc Sine Hyperbolic Arc Sine Arc Tangent Hyperbolic Arc Tangent Round to nearest integer Square Cosine Hyperbolic Cosine Exponential e Common Logarithm Natural Logarithm Maximum of nl n2 Minimum of nl n2 Random number between 0 et 1 Pi 1 Next largest integer Next smallest integer Powers of 10 square Root Sign Sine Hyperbolic Sine langent Hyperbolic Tangent Absolute Value Modulus Syntax ARCCOS value arccos acos ArcCos ARGCH value argch ArgCh ARCSIN value arcsin asin ArcSin ARGSH value argsh ArgSh ARCTAN value arctan atan ArcTan ARGTH value argth ArgTh ROUND value round Round SQR value sqr SqrQ Sq COS value cos Cos COSH value cosh CosH ch EXP value exp Exp log10 value Log10Q lg LN value InQ Ln MAX valuel value2 max v1 v2 Max vl v2 MIN valuel value2 min v1 v2 Min v1 v2 Random random Rand rand rt II PI
19. ault axes Select also the grid interval to obtain a set of points at unit intervals Select Define Grid in the Draw toolbox then click on the axes to display the grid Construct a straight line L passing through two points of the grid and call up its equation using Equation and Coordinates from the Measurements toolbox You can move the points which define the straight line from one place on the grid to another Note that its equation updates automatically The line could equally well be defined by points not on the grid Choose a new set of axes so that L becomes y 0 Use New Axes from the Draw toolbox Construct a circle defined by two grid points and call up its equation in both axial systems Click on the curve then on one of the axes 25 2 Area problems Here is an example which considers how an area varies A curve s obtained as a locus of the point whose abscissa is AM and whose ordinate is the area of the trapezium shown These measurements are transferred to the axes by means of Measurement Transfer from the Constructions toolbox 179 cmq B Variation of the area of trapezoid AMNC according to the position of M on segment AB 111 8 Graphical Representations of Functions Although Cabri is primarily a geometry package it can also be used to show rapidly different examples of the graphs of functions and to consider the influence of their various parameters on the graphs Here is an example
20. ct point or intersection point e A wide variety of messages linked to the cursor keeps the user informed 5 1 2 Additional Geometric Tools A number of geometric tools have been added notably 1 3 Rays half lines vectors rregular polygons and regular polygons Conics defined by 5 points and circular arcs The sum of two vectors a compass The transfer of a measurement to a half line a vector an axis or a circle A locus has become an object upon which points can be created as the result of a macro construction It is updated following displacement Transformations have been added translation rotation enlargement inversion Line symmetry and rotational symmetry have been separated A full range of analytical geometry tools is available cartesian systems of axes creation and modification of systems of axes coordinates of points equations of lines circles and conics in several systems of axes a grid of points at integer intervals and polar coordinates Other Tools Construction macros one of Cabri Geometry s strengths are more powerful and more flexible to use initial objects and their images can be declared separately then revisited to edit the initial and final objects and when the whole construction is complete the macro can be validated Image objects can be of different types measurements calculated values etc A macro can have a multiple definition with several initial objects for the same con
21. d a point M on this segment Cl A Construct a circle C1 with centre M and the perpendicular to AB which goes through M Mark P as one of the points of intersection of this line with the circle C1 Construct the circle C2 with centre P and radius PM Hide C1 and measure the distance AM Use Distance amp length from the Measurement toolbox by clicking on A then M To transfer the arc length AM on the circle use Measurement Transfer from the Construction toolbox by clicking successively on the number the circle and the initial point for the length which is M here You will obtain a point R You will notice that the measurement is drawn n the anticlockwise direction from M To go in the other direction from M construct the point which 1s symmetric to M with the perpendicular to AB as the axis of symmetry Call this point V u E A 1 Sr cm M Hide the perpendicular to AB and the point R Construct the locus of V as M moves along AB You will get a cycloid v as FA 1 97 com M E An astroid similarly you can construct an astroid by rolling a circle along the interior of another circle and transferring arc lengths We leave you the pleasure of constructing this for yourself You can also leave the radius of the interior circle variable by moving the centre of the circle you will obtain a family of hypocycloids 111 6 Some Transformations Translation Rotation and Enlargement
22. defined by a number to a half line a vector an axis or a circle in the anti clockwise direction Construct a locus or an envelope A point or object is selected for which the locus is required then a point on which it is dependent which is constrained to move on an object Redefine the geometrical characteristics of a point The options are available on a pop up menu Redefine the geometrical characteristics of an object a point line circle conic etc The options are available on a pop up menu Construct the mirror image of an object Select first the object then the axis of symmetry Construct the image of an object under a half turn Select first the object then the centre of rotation Construct the image of an object under a translation Select first the object then the translation vector 30 E Rotation el Dilation ci Inversion 7 Macros AAA Z Initial objects Final objects Define a Macro User defined macro 8 Properties T Collinear Parallel Perpendicular Equidistant Member Construct the image of an object under a rotation First select the object then the centre and an angle defined by a number Construct the image of an object under an enlargement First select the object then the centre of enlargement and a scale factor defined by a number Construct the image of a point under inversion Select the point and the circle This enables initial objects of a construc
23. e icon hint etc of an existing macro can be modified similarly A construction macro which has been saved can at any time be placed in a toolbox using Open from the File menu Look for files of type MAC or sometimes TXT or DOC if the macro has been edited in a word processing package or comes from another type of computer Macintosh files do not have filename extensions so select the All Files option in Windows to open them A geometrical diagram in Cabri is always saved and reopened with all of its associated Macros The Cabri II CD ROM contains a library of pre recorded Macros The configuration of the tools that you create are also opened with the Macros that were present when they were created This 1s convenient for keeping together macro libraries with the same theme macros for conics or for vectors for example 17 III 4 A Locus Pascal s Limacon Construct any circle centre O Mark a point M on the circle and at M construct the tangent to the circle P is any fixed point and H is the foot of the perpendicular from P to the tangent Construct the locus of H as M moves around the circle In the Construction toolbox select Locus in the drawing select first H then M This defines the locus Pascal s lima on Move M and observe the changes n the locus The locus is a Cabri object on which a point can be marked A point on an object When the various parts of the diagram are moved the locus update
24. eacher can change the tools which are available to the students by suppressing various menu items and by adding other macros of their own The new tools thus created can be saved and when selected will also load the relevant macros e Tools such as Hide Show have now been improved so that colour width and line style can be changed The shape of points can be modified In addition angles and line segments can be marked in different ways without being taken up by the software at the level of coherence with the diagram 1 4 Editing e The display of text and numbers can be changed size colour font style border background not in DOS version e The possibilities for redefining points and objects Windows has been extended II Installation Circle circumscribed with a triangle on the pseudosphere Yves Martin II 1 System Requirements Cabri Geometry II runs under either Windows 98 SE 2000 ME XP NT or Apple Macintosh System 6 or higher Cabri Geometry II occupies 1 5 mb of disk space and requires at least 4 mb of RAM II 2 Installation The Cabri Geometry II installation program on your CD ROM will automatically install and place the necessary components in the correct places on your computer Upon installation you are asked to choose which language you wish to use You can change this later if you wish Installation on a network in common with other software requires direct access to the server when fi
25. ed are the same as those for the most recent printout If the user has not printed a previous drawing the Cabri II default settings are used 49 The operation of Copy Paste to A Cabr drawing Any object which is selected for Copy can be pasted into another Cabr drawing In the same drawing the elements that have been copied are slightly displaced to avoid superimpositions It 1s not possible to copy a table nor its constituent parts A document in another application Only the contents of the selected rectangular area will be copied to the Mac clipboard for pasting into the Scrapbook or other type of document If an element geometrical shape text or table 1s partially selected by the rectangle only the part inside the rectangle is copied The insertion of an 1mage into Word 6 or later can be made easier holding down the Shift key then using the mouse to drag the edges of the image means that each edge can be adjusted independently of the others Special objects Trace 1s not an element of a drawing and so 1s neither copied nor printed Special display for Back projection does not affect the result of either Copy Paste or printing This type of display is obtained by clicking on the Help icon while holding down the Alt key Inserting a diagram into a document to be published To get a good quality print for a diagram which 1s inserted n a text document it is possible to use an encapsulated PostScript file EPS file For t
26. ema Distance and Length Area Slope Equation and Coordinates Calculate 4 E Angle 8 Tabulate 10 Display All Label Al Comments Numerical Edit IE amp Mark Angle Fix Free vl Trace On Off yel Animation Measures the length of a segment the distance between two points the circumference of a circle of a conic or of a polygon The units can be changed and on Macintosh only the size font and style of the value displayed Measures the area of a circular disc an ellipse or a polygon The units can be changed and on Macintosh only the size font and style of the value displayed Displays the gradient of a line relative to the x axis by default The size the font and the style can be changed except in DOS Displays the size of an angle defined by three points the first point 1s on one side then the vertex then a point on the second side or by its arc The units can be changed also the size the font and the style except in DOS Gives the equation of a line a circle or a conic relative to the existing reference system by default or to a reference system selected before requesting the equation The type of equation polar or cartesian can be changed as can the size font and style except in DOS Displays a calculator upon which calculations can be carried out using numbers from the keyboard or values taken from the diagram Displays a table into which successive numerical values ta
27. g om tre version 1 6 Cabri geometre MS DOS version 1 7 and Cabri g om tre Macintosh version 2 1 Cabri Geometry II has many extra functions compared to the earlier version The direct manipulation of geometrical constructions is still one of its main features I 1 General Operation The general working area is easier to use e Menus have been replaced by toolboxes which are accessed via icons The tools are grouped differently points lines curves construction tools transformations macros properties measurements miscellaneous edit e Objects selected in a toolbox remain active until a new tool is selected This avoids for example having to select segment repeatedly when drawing a succession of segments e Objects can also be selected in order to edit them in various ways such as changing line thickness or colour etc An object which has been selected can also be deleted by pressing the backspace key on the keyboard e Objects such as a line a segment a triangle or a polygon can be manipulated as single items and not just as the separate points from which they are made e The selection arrow can be used to transform objects parts of lines as well as triangles polygons and conic sections etc in the working area by translating rotating about a point or enlarging e Cabri II mostly picks up the user s intention to mark a point on an object or a point of intersection Cabri II shows the type of point obje
28. his the following must be available e aprinter with the PostScript facility e aprinter driver which can generate such a file for example the driver for a LaserWriter 8 in OS 7 5 e a word processing package which will accept the insertion of a diagram The stages are as follows In Cabr Open the Print window Using the Placement Options button block the part of the diagram required against the top and left of the print area In the same window select File as the destination instead of Printer In the next dialog box select format EPS and save it The diagram is then saved as an EPSF In the Text insert the diagram using the previously saved form in the desired position It can then be cropped and or reduced whilst keeping the PostScript quality printout It is essential for the same printer driver to be used in the final printout as the one which has been used to prepare the encapsulated image It is possible to install the driver on a machine which is not linked to the printer which will be used for the final printed version Reminder in Word 6 or later it is possible to adjust each edge of the image independently of the others by holding down the Shift key while dragging an edge 50
29. i distributors Chartwell Y orke at http www chartwellyorke com Cabri figures by Yves Martin are available on the site http www w cabri com abracadabri Initial Text by Bernard Capponi Revision Eric Bainville Illustrations Eric Bainville Yves Martin Sylvie Tessier English translation Sandra Hoath Copyright 2001 Cabrilog S A S Chartwell Yorke Except for Windows files which cannot be read by DOS There is an update for the Macintosh version which enables it to read files from the Windows version This can be downloaded from the Cabri website at http www cabri com 2 Contents Aperiodic tiling Sun Sylvie Tessier after Penrose I FROM CABRI GEOMETRE TO CABRI GEOMETRY Il c ccccccscssscsssssssssssscssessssssscsseseseees 5 MELLE Sas atl Bere AO een m 3 12 Addons CORN UIC Bore NORUNT 6 e OBER OO ee ea ee En m 6 BC dE eia RT ue 7 II ASEA CLEAT IIN o A E EEE A 8 ESS nea Regurem iS RT IRR RR 8 I 2 is CANINA ON ee ee ee ee 8 HI FIRST STEPS IN CABRI GEOMETRY L 0000000000000000000ssuuu00s0sssnunnssssssnnunsssssssnnensssnse 9 MEI The Cabri Geometry a er 9 W TES EO ONO AU ae ee O EUM BIO OUUEE 10 II 5 Trangle based Construell on ae u ar 11 IT SW Uds ec REGI IR 18 III 5 Measurement Transfer Using the Cycloid as an Example eese 19 III 6 Some Transformations T
30. ibed circle or of the centroid as standard constructions which will then become available to all future constructions from a toolbox the default toolbox is Macros but it can be changed by using the menu item Tool Configuration from the Options menu list To achieve this a construction macro must be recorded based on the figure created H Hao amk aga az We shall create a construction macro for the Centroid The diagram that you have constructed to demonstrate the centroid of a triangle must be on the screen Select the Ke icon which enables the initial objects to be determined 15 Select the initial objects here just the triangle The selected objects flash to remove them from the selection merely click on them a second time From the same toolbox select the Final Objects icon sY Select the centroid Selection deselection is the same as for initial objects Still in the same toolbox select Define Macro Enter the name of the macro in the box Define Macro Name of the construction New construction Name for first final object M Help for this macro The appearance of the dialog box in the Windows version Note that any hint that you write is intended for future users who will access it via S or the help menu or other messages You can also create an icon for the macro This icon will appear on the Toolbar in the same way as other toolbox items Name
31. imetres Alt or Option or Ss Macintosh e When creating a straight line a ray or a circle the Alt or Option key forces a second free point to be created dynamically In this way one obtains circles with a centre point and a point on the circumference or straight lines through two points n Hide Show The if key allows access only to those objects which are not hidden It filters out selection of hidden objects vf 5 lef allows only hidden objects to be selected The selection of others is filtered out 43 In Polygon regular polygon triangle The Alt or Option f key enables the distance to be measured round part of perimeter determined by two points of the polygon vertices or points on the sides going in the direction in which the polygon was created Example y C Measure the length of the bold segments in the direction in which the polygon was created During the drawing of lines which are parallel or perpendicular to a side of a polygon or a triangle the Alt or Option Ss key enables the user to select the direction held by a point and which will change therefore according to the position of the point on the polygon Example F Z The perpendicular to the side AB passing through U will be perpendicular to whichever side contains U as U is moved around the polygon e To increase the thickness of construction lines in a Cabri II diagram for example to make them clearer for back pro
32. ing the mouse VI 1 With the Mouse Double click A double click 1s used to enter the edit mode for labels numbers comments the calculator and tables Holding down the mouse button click and hold eOn a tool icon opens the associated toolbox eWhen the pointer tool 1s active this causes the basic points to flash as well as the points on an object in a diagram points which one can move directly with the mouse Moving the mouse whilst holding down Ctrl or amp xl Moves the figure around the page V1 2 With the Keyboard Warning on the Macintosh the key is generally replaced by 4 f and the n key by 1 1 Classic menu shortcuts are shown alongside the items in the menus and are shown in part IV idi F is the only menu command which is specific to Cabri II and corresponds to Full redraw drawing update and removal of traces a with dragging the mouse enables the drawing area to be moved in relation to the window On the PC only the choice of units for measurements and numbers entered from the keyboard is initiated by f U On the PC clicking on the calculator displays the calculator window If this 1s followed by a double click on the result of a calculation which is displayed in the drawing area the associated formula is re displayed in the calculator window Escape Le f Abandons the current operation and returns to the translation pointer In dialog boxes it is equivalent to C
33. item Triangle from the Line toolbox N HN Abel ll adj Line Segment Hay Vector Triangle Polygon Regular Polygon Regular Polygon You will see as you move the pointer down the list that the picture on the icon changes and once triangle has been selected the picture AJ stays as a triangle The cursor in the drawing area 1s shaped as a pencil p click with the mouse when the pencil points at the desired position for A enter immediately on the keyboard the label for the point A click for the second point again enter the label on the keyboard B and similarly for the third point Note This method of naming points on the fly 1s easy and quick but it does not allow the user to correct any typos it 1s also limited to five characters for the label 11 Changes to the label can be made using the Name item in the Text toolbox Al E e To move the label for point A select the pointer tool k from the Pointer toolbox Triangle remains the active tool and f you click on it you will start the construction of a new triangle You can also press the key to activate the Translation Pointer La Move the pointer close to the label A Cabri displays the message This label click and drag the mouse to move the label Move translate it so that it is not on top of any of the sides of the triangle B E A T A e e The triangle can be moved or changed in shape To move a
34. jection on the Macintosh one simply clicks on the 13 balloon which 1s on the title bar for the diagram while holding down the i key For a printout using PostScript it is possible to get extra fine lines by holding down the Alt or Option Ci key when clicking on OK in the Print dialog box This modification can only be carried out on fine lines Macintosh only 44 Arrows 5 l l LI In the general environment If these keys are not used in an active tool such as Label Comments Numerical Edit or Calculate then The f and I arrow keys move from one active menu on the toolbar to the next The Lt and arrows move up and down the menu to change the active item When editing text The and arrows move the cursor along the line of text 1n the chosen direction while the It and 4 move the cursor from one line to the next When editing numbers The left and right arrows move the cursor from one digit to the next For the Macintosh only the f arrow will display extra decimal places up to 15 significant figures For numbers created with the Numerical Edit tool the bi and Li arrows increase or decrease in unit steps the digit which is immediately to the left of the cursor If more than one digit is selected both are changed simultaneously c Enter Carriage return or BH on the Macintosh These keys confirm actions in the same way as does clicking on OK in a dialog box
35. k selects the tool displayed All the icons available from the toolbox are shown 1n the following lists 28 1 Pointers hf Pointer iki Rotate X Dilate ixi Rotate and Dilate 2 Points Point l Point on an object Intersection Point iS E E I I I IC 5 Straight Line Segment Ray Vector Triangle Polygon Regular Polygon select and move objects translation Rotate an object about its centroid or a point Enlarge or shrink an object about its centroid or a point simultaneously rotate and enlarge an object about its centroid or a point Mark a point either on an object or at the intersection of two objects Mark a point on an object Mark one or more points at the intersection of two objects Construct the straight line defined by a point and either a direction selected by a second click or a second point Construct the line segment defined by two points Construct the ray half line defined by a point and a direction or a second point Construct the vector defined by two points Construct the triangle defined by three points Construct the polygon defined by n points Construct a regular polygon defined by a point at its centre a first vertex for the long radius and a second vertex to fix the number of vertices and the number of turns for star polygons with intersecting sides For a convex polygon the rotational sense 1s clockwise and the number of sides is selected by mouse click Fo
36. ken from the diagram can be placed The table does not update with the diagram However it can be copied into other software spreadsheets word processors The Tab key enables a line in the table to be selected Names points lines or circles by means of a label which can be text The size the font and the style can be changed except in DOS Enables text to be added Variables from the diagram can be included The size the font and the style can be changed except in DOS Enables a number to be entered The units as well as the size the font and the style can be changed except in DOS Marks an angle with an arc The type of arc can be changed Fixes and unfixes the position of a point which then cannot be moved Its name and its attributes can no longer be changed until it is unfixed Produces or suppresses the outline of an object during its displacement The trace cannot be manipulated Moves objects automatically The animation 1s started by stretching and releasing a spring 32 ui Multiple Animation 11 Draw Hide Show mt Es Ni Colour al Fill 2 Thick e Dotted xl Modify Appearance 1 Show Axes Hide Axes BY um New Axes Define Grid IV 3 Calculator Moves several objects automatically Springs are put in place and the animation 1s started from the keyboard Hides or shows the objects in a diagram Enables the colour of an object to be chosen Fills polygons circles and te
37. nce Printing The following options are available in the dialog boxes e Page Setup paper size enlargement reduction portrait landscape e Print number of copies colour black and white name of author name of drawing date Changing these options when there is no drawing open or while the working area has still not been saved deals with the default Print settings for Cabri II 1 e the original settings when opening Cabri II or at the start of a new drawing When a drawing is saved the settings used are the same as those for the most recent printout If the user has not printed a previous drawing the Cabri II default settings are used When printing in Black and White it is preferable to make the lines in the drawing black or a dark colour otherwise the dot spacing used by some printers for grey tones will make the lines appear wavy If a drawing includes a grid the printout will take take much longer Copy Paste to other applications While the a pointer is active select an area and copy it It is also possible to Paste a sheet into Cabri but not all of the relationships will necessarily be maintained The philosophy of Cabri is rather to encourage the use of Macros as tools to reproduce constructions e The Copy Paste tool operates in object mode and the drawing which is pasted into another application can be split into ts separate parts such as points lines polygons circles arcs conics loci text a
38. nd tables e However some remarks must be made about the way that various current software treats these objects in most applications that will accept Cabri II drawings dotted lines are not visible on the screen but they are reproduced in printouts if the printer used will accept PicComments the locus of points or lines is a single object and it may not be possible to separate out the independent points or lines in the software to which the drawing has been copied 48 n MacDrawPro further remarks are needed Dotted Lines dotted lines are drawn for all straight line objects but are gnored for all curved objects both on the screen and when printed Line thickness fine lines appear on the screen as identical to medium lines The difference can be seen in a printout or if the drawing 1s enlarged Partial selection of text or polygons a filled polygon or a disc which is partially selected is completely filled after pasting however only the selected part of the drawing 1s reproduced It is similar for text a partially selected text is pasted in its entirety MacDrawPro 1s unable to interpret the character 2 as used by Cabri II as an index in an equation It is possible to increase the size of this character then move it to improve the appearance of the equation Remarks concerning Printing and Copy Paste in Cabri II on the Macintosh Printing Printouts are done in such a way as to make best use of
39. on of Two Objects in order to construct this type of point You can label this point on the fly H for example The construction of the orthocentre is achieved by marking the point at the intersection of the altitudes but since there are three altitudes Cabri requests further information with the message Intersection of Using the mouse button the choice is made between the three lines three altitudes and the orthocentre will appear as a point Label this point on the fly or by using the menu item Label in the Display toolbox B Point at this intersection You can select this point but it cannot be moved using the mouse It 1s the same for all points which have been obtained as the result of a construction The selection of the point allows it to be deleted or to have its attributes colour or shape changed A LULE This Line This Line This Line 13 4 Construction of the medians of the triangle and its centroid To construct the medians of this triangle start by marking the midpoints of the sides by selecting the Midpoint tool from the Constructions toolbox x ANg Has da mi gd Bergen sr TE RN Midpeint _ Perpendicular Bisector Vector Sum Compass Measurement Transfer Locus Redefine Object Next select a side of the triangle or two vertices to construct one mid point The mid point tool 1s still selected so the midpoint of the other sides can easily be B
40. or led then using Backspace 1 Construct any triangle ABC and a point O which will be the centre of enlargement Enter a number 1 5 for example Construct the image of the triangle under enlargement centre O scale factor 1 5 Dilation from the Transformations toolbox During the construction make sure that the Cabri messages are followed Change the scale factor see previous section and the position of the centre of enlargement O 1 5 A B You can also use the length of a line segment as the scale factor and then the scale factor is changed simply by extending or reducing the line segment 4 Transformations in general All transformations except inversion act not only on points but also on segments straight lines triangles polygons circles or conics Inversion only transforms points To obtain the inversion of a triangle for example take a point on the triangle construct its image under inversion then call up the locus of the transformation as the original point moves round the triangle 22 E Triangle ABC and its Inversion in the Circle With students for them to discover the images of objects such as segments lines or circles under a transformation it 1s often interesting to use the same approach even though Cabri Geometry constructs 1mages directly 111 7 Analytical Geometry Straight Lines Circles 1 Reference systems and equations select Show Axes in the Draw toolbox to show the def
41. r star polygons the rotational sense 1s anti clockwise and the number of sides and revolutions 1s selected by mouse click A pentagram is a 5 2 star polygon 29 4 Curves 5 C Circle Constructions Perpendicular Line Parallel Line Midpoint Perpendicular Bisector Angle Bisector Vector Sum Compass e E Be EE IC s Measurement Transfer We Locus He Redefine Point Macintosh and DOS Redefine Object Windows V Transformations A Reflection e Symmetry x Translation Construct a circle First select an existing point or create a new one then select the size of the radius by clicking on a point on the circumference Construct an arc of a circle defined by three points the two end points and a point in between Construct the conic defined by 5 points Construct the line passing through a point perpendicular to a given direction Construct the line passing through a point parallel to a given direction Construct the midpoint of two points or of a segment Construct the perpendicular bisector of two points or of a segment Construct the bisector of an angle defined by three points or by its arc Construct the resultant of two vectors First select the two vectors then the origin for the resultant Construct the circle defined by a length and point Choose first the radius length by selecting a segment or two points then select the centre Transfer a measurement
42. ranslation Rotation and Enlargement cccccssesssseseeeeseeseeeseeeeeeeees 20 III 7 Analytical Geometry Straight Lines Circles uuuueeeeesseeesesssssnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn 23 III 8 Graphical Representations of Functions 00sssssssesssssnennnsnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnsnnnnnnnnn 24 IV CABRI GEOMETRY II KEYBOARD AND MENU FUNCTIONS e eene 26 IEEE 2 22 2 see c 26 IV 2 Tb Toolbar nee een 28 VI erum Ep 33 IN dX uriDutes Tooli esne np PIE D ED PM Cp Mu tM UM 35 Parse le I 1 NACER MEER PE RES 35 Ve CONFIGURING THE SOFTWARE 2225 36 Vol Pretere ne sun een see ie ss iu re 36 Mee Detaule Setune Machtiosh ony uses ese E Ancien EAE CE et e MM eM C E 38 V5 Comlicurine tne Tool et ce 38 V4 Replay E Ma E NE T seele 40 VI SHOR EGENT 42 MET Ww he Mouse teens 42 NME2 Wih he Keyboar doerien einen nee 42 VII EDITING AND PRINTING DIAGRAMS eeessseeeccssecccssecccssecccssecccosecccssececssecocsseccocosececsseeoso 47 BAUM ER AIMER m O T I eee 47 NIE Macintosh verston Only ee T Ei 48 I From Cabri Geometre to Cabri Geometry II Tiling the plan with squares and hexagons Eric Bainville after P Blum and F Bertaut Cabri Geometry II is the result of a complete respecification of the earlier version of Cabri
43. re being more than one method to colour an object each user can choose the method which suits them best Ep Colours O mi mi mi mi mi Thickness E nm m m Line Style L1 ee Point Symbol al ER ERO Angle mark TATT Segment mark ER Reference system Text style LE TEN PSL C IV 5 Style Palette This palette 1s available from the item Modify Appearance in the Draw toolbox It enables the appearance of certain objects such as points or the symbols used to indicate angles or equal lengths to be changed It s also possible to swap between cartesian and polar reference systems or to change the appearance of text with a border or a colour fill During the current session only To keep these changes see the defaults in the next section 35 V Configuring the Software V Be Tiled Pentagons Eric Bainville after K Reinhardt The three items Defaults Preferences and Tool Configuration enable the software to be configured in response to the needs of the user particularly when setting up teaching sessions by suppressing some items but adding others as construction macros V 1 Preferences 1 Windows version The same defaults and preferences that are available in the Macintosh version are in one single Preferences window accessed by choosing preferences from the options window Cabri II enables default preferences to be chosen to configure the software accuracy of measurement equation type colours
44. rst running it and then when preference files or language initialisation files are created II First Steps in Cabri Geometry II Tiling the plane with one hexagon Eric Bainville after K Reinhardt The following pages offer some examples which illustrate the main functions of Cabri Geometry II which you can learn about by constructing the diagrams whether or not you have already met Cabri Geometry These examples do not claim to be original they have been chosen to demonstrate the use of the software 111 1 The Cabri Geometry II Screen The Cabri II screen shown overleaf illustrates The standard menu bar The toolbar which provides all the tools needed for constructions Each icon corresponds to a tool and produces an extended toolbox if the mouse button is held down The properties bar on the left of the screen The colour palette which can be positioned anywhere on the screen The scrollbars for moving around the drawing area a Im square A diagram with measurements of area and length and a calculation based on these numbers Note that these measurements and calculations are updated each time an element of the diagram is moved as in Cabri g om tre I 4 Cabri g om tre Il Figure 1 EI File Edit Options Window Help I8 x A AND Hada BEE Result 1 09 AHEL ENE BE J B m m mij mm m j jsm Colour III 2 The Toolbar Most of Cabri Geometry s
45. s accordingly However one still cannot locate the intersection of a locus with another object nor obtain the equation of a locus One can however build a construction macro for which the image is a locus Try with Pascal s lima on Initial objects the circle and the points M and P image object the limacon The number of points which create the locus 1s limited to 50 linked together For this reason the locus can be segmented You can increase the number of these points by selecting the locus and using the Gg key You can also use Preferences from the Options menu to change the default values for loci Preferences 2Ix Display Precision and Units Coordinate System and Equations Loci Options Default Styles Geometry System Options Number of objects in locus m Locus of points IV Link points Locus of lines IV Envelope Selecti Factory Settings Apply to 2 ee Keep as defaults Save to file Close Preferences Windows version preferences for loci 18 111 5 Measurement Transfer Using the Cycloid as an Example Cabri Geometry II enables measurements to be made of half lines vectors axes or a circle and then transferred to other diagrams In this way numbers such as measurements of lines angles areas or numbers entered using Number from the Display toolbox can be transferred We shall use a measurement transfer from a circle to construct a cycloid Construct a segment AB an
46. struction For example for the circumscribed circle of a triangle 3 vertices can be defined as initial objects as well as the triangle itself Check property displays a message which tells the user about certain properties of the figure such as parallelism perpendicularity collinearity equidistance from points or whether a point belongs to an object Changing the figure causes the display to change if the property is no longer true Units of measure for length and area can be chosen by the user A calculator enables various calculations to be carried out using numbers which originate either from the keyboard or from the figure measurements or values from calculations AII the standard functions of a scientific calculator are available with some additional functions such as the maximum or minimum of two numbers Numbers can be entered for example to fix the scale of an enlargement the angle of rotation or to choose a particular measurement These numbers can be changed and the construction follows suit Text can be added to the diagram which can include numbers linked to the diagram A point can be permanently fixed pinned The path of an object trace can be shown over a displacement The trace function 1s distinct from locus A diagram can be animated automatically by moving points or objects by means of springs which are stretched and relaxed Thus on completed objects there can be continuous animation e The t
47. tion macro to be defined Enables the final objects of a construction macro to be defined Having defined the initial and final objects this validates the macro names it creates an icon and a help message Saving to disk is suggested If the name of an existing macro 1s chosen it can be replaced This button is a new tool defined by a user created construction macro It is labelled with the initial letter of the macro here N Macintosh The user can also create the icon In Windows the default name is New Construction Displays a message to confirm or contradict the collinearity of three points The text is updated according to the relative positions of the three points Displays a message to confirm or contradict the parallel direction of two lines half lines segments or vectors The text is updated according to the relative directions of the objects Displays a message as to whether two lines half lines segments or vectors are perpendicular The message is updated according to the relative positions of the objects Displays a message as to whether a point 1s equidistant from two other points The first point selected is the one to be tested relative to two other points The message is updated according to the relative positions of the objects Displays a message to confirm or contradict whether a point belongs to an object The message is updated according to the relative positions of the objects 3l 9 Measurements
48. tools are accessed from the toolbar The icons open different toolboxes Pointers Points Lines Curves onstructions Y ONO Huy ey s Transformations _ Macros Check Properties Measure Display Draw In the following text the toolboxes are described by the labels which are shown n the llustration above Refer back to this diagram as necessary To select a construction tool from the bar double click on the corresponding icon Each toolbox contains several items to obtain a tool which 1s not shown as an icon click and hold on the associated icon then drag the mouse to select the tool from the menu list which appears Hints Don t forget that you can always find hints about the tools you are using by clicking 1 Macintosh or using EZ PC A text message appears at the bottom of the window For example if the Jn icon is the active one on the toolbar you will get the following message Generates the coordinates of a point or the equation of a line circle or ellipse The hints relate to the tool Sometimes hints for using the tool are included when its use presents particular difficulties 29 66 e Messages such as this point perpendicular to this line etc are displayed close to the cursor Often they give information about the diagrams and the current procedure 111 3 Triangle based Constructions 1 Construction of triangle ABC Construct a triangle using the menu
49. ursor Sr messages which Cabr displays You can E change the angle of rotation by changing the number that has been displayed definitely the easiest method is to double click on the number and use the arrow keys lo Ll In the Windows version double clicking on the number when Numerical Edit is selected causes arrows to appear at the right of its window These arrows act on the selected digit of the number or by default on the digit which is to the left of the cursor With the number selected one can also change it automatically using Animation from the Display toolbox Unit selection Macintosh You can also vary the number by selecting it then a digit tens units tenths etc and using 11 to increase it or to decrease it You will see immediately the effect on the rotation It is also possible to choose the angle of rotation from the diagram by measuring a modifiable angle This angle can then be changed in order to change the angle of rotation A spring appears By pulling the spring downwards then releasing it increases the number while by pulling the spring upwards and releasing it the number is decreased The digit which is changed is the one corresponding to the latest position of the cursor in the number 21 3 Enlargement dilation You are now going to enlarge a drawing Delete the current drawing by using Select All from the Edit menu or by using the key combinations SER A
50. xt in the colour chosen from a palette Changes the thickness of lines Changes the line style dotted etc Changes the appearance of certain objects points angle arc line marks type of axis text Shows the default system of axes Hides the default system of axes Enables a new system of axes to be defined Displays a grid for a reference system The grid 1s an object upon which points can be marked The type of grid depends on the reference system ao ej Ee e z The calculator enables calculations to be carried out on values coming from the diagram measurements displayed numbers calculation results or entered from the keyboard When the diagram is altered the measurements and the calculations are instantaneously updated The results are displayed temporarily at the right of the calculator window In order to save the answer it must be copied to the drawing In the calculator window click and drag the answer to the point in the drawing where it 1s to go Calculation line Answer aa O ug innlolalalgjen 33 The calculation which has led to a particular displayed answer can be re entered in the calculation line To do this e On the Macintosh double click on the answer and click on the box i isip RUi sle s labelled Calc to display its corresponding calculation in the calculation line of the calculator Result 174 85 c n On the PC double click on the answer the calcul
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