Casio Geometry manuale d’uso

http://edu.casio .com Add-in application f or fx-9860G series/ E GRAPH 85 series calculator s Geometry User’ s Guide[...]

20060601 Contents Contents 1 Geometry Mode Overview 2 Drawing and Editing Objects 3 Controlling the Appearance of the Geometry Window 4 Using T ext and Labels in a Screen Image 5 Using the Measurement Bo x 6 W orking with Animations 7 Error Messages[...]

20060601 1-1 Geometry Mode Over view 1. Geometr y Mode Overview The Geometry Mode allows you to dra w and analyze geometric objects. Y ou can draw a triangle and specify values to change the size of its sides so the y are 3:4:5, and then check the measurement of each of its angles. Y ou can also lock the coordinates of a point or the length of a li[...]

20060601 1-2 Geometry Mode Over view k 1 e (View) T o do this: Select this menu item: Star t a box z oom operation 1:Zoom Box Enter the pan mode (page 3-3) 2:P an Enter the scroll mode (page 3-4) 3:Scroll Enlarge the display image 4:Zoom In Reduce the size of the displa y image 5:Zoom Out Adjust the size of the displa y image so it fi lls the disp[...]

20060601 1-3 Geometry Mode Over view k 4 (Construct) T o construct this: Select this menu item: A perpendicular bisector 1:P er p Bisector A perpendicular 2:P er pendicular A midpoint 3:Midpoint An intersection 4:Intersection An angle bisector 5:Angle Bisector A parallel 6:P arallel A tangent 7:T angent k 5 (T ransform) T o do this: Select this men[...]

20060601 1-4 Geometry Mode Over view k K (Option) T o do this: Select this menu item: Input text 1:T ext Input an expression 2:Expression Specify the number f or mat Geometr y Mode measurements 3:Number Format Unlock all measurements 4:Clr Constraint Display all objects 5:Show All Hide the currently selected object 6:Hide Using the P ointer Y ou ca[...]

20060601 1-5 Geometry Mode Over view Using Ke y Help Pressing 1 (File) – 4:K ey Help or the a ke y will display K ey Help , which provides information the function of each ke y in the Geometr y Mode. Use the c and f ke ys to navigate between the three K ey Help screens. T o exit the K ey Help screens, press J . Note The ke y operations shown on t[...]

20060601 1-6 Geometry Mode Over view u T o open an existing fi le 1. P erform the follo wing operation: 1 (File) – 2:Open. • This displays a men u of e xisting fi les. 2. Use c and f to mov e the highlighting to the fi le you want to open and then press w . • The follo wing dialog box will appear if you ha ve a drawing on the screen. 3. T [...]

20060601 1-7 Geometry Mode Over view u T o save a fi le under a different name 1. While the fi le you w ant to sav e is open, perform the following oper ation: 1 (File) – 3:Sav e as. • This will display the fi le name input screen and automatically s witch the calculator’ s keys to Alpha Lock. The cursor changes to 0 when the ke yboard is [...]

20060601 1-8 Geometry Mode Over view Ke y Functions The fi gure below shows the k eys that are used f or Geometr y Mode dra wing screen operations. Displays men us. (P age 1-1) Selects an entire polygon. (V alid for polygons only .) (P age 2-8) Displays K ey Help . (P age 1-5) Selects, deselects, ex ecutes. Selects, deselects, ex ecutes. Zooms in/[...]

20060601 2-1 Drawing and Editing Objects 2. Drawing and Editing Objects This section explains ho w to perform the following oper ations. • Plot points , draw line segments, polygons, etc. ([F3](Draw) menu) • Select and deselect objects ([F2](Edit) men u) • F or a drawn object, construct a per pendicular bisector , per pendicular, etc. ([F4](C[...]

20060601 2-2 Drawing and Editing Objects u T o add a labeled point to an existing line Note Y ou can use the follo wing procedure to add a labeled point to an existing line, to a side of a polygon, to the peripher y of a circle, etc. 1. P erform the follo wing operation: 3 (Draw) – 1:P oint. 2. Mov e the pointer on the screen towards the line whe[...]

20060601 2-3 Drawing and Editing Objects u T o draw an infi nite line 1. P erform the follo wing operation: 3 (Draw) – 3:Infi nite Line . 2. Mov e the pointer to any location on the display and then press w . 3. Mov e the pointer to another location on the display and then press w . • This will draw a line that passes betw een the two points.[...]

20060601 2-4 Drawing and Editing Objects u T o draw a circ le 1. P erform the follo wing operation: 3 (Draw) – 6:Circle . 2. Mov e the pointer to the location on the display where you w ant the center point of the circle to be and then press w . 3. Mov e the pointer to the location on the display where you w ant the circumference of the circle to[...]

20060601 2-5 Drawing and Editing Objects u T o draw a triangle 1. P erform the follo wing operation: 3 (Draw) – 8:T riangle. 2. Mov e the pointer to any location on the display and then press w . 3. Mov e the pointer to another location. • This causes a selection boundar y to appear , indicating the size of the triangle that will be drawn. 4. P[...]

20060601 2-6 Drawing and Editing Objects u T o draw an isosceles triangle 1. P erform the follo wing operation: 3 (Draw) – 9:Isosc T riangle. 2. P erform steps 2 through 4 under “T o draw a triangle” (page 2-5). • This draws an isosceles triangle. u T o draw a rectangle or a square 1. P erform either of the follo wing operations: 3 (Draw) ?[...]

20060601 2-7 Drawing and Editing Objects u T o draw a polygon 1. P erform the follo wing operation: 3 (Draw) – C:P olygon. 2. Mov e the pointer to the location on the display where you w ant a ver tex of the polygon to be and then press w . • Repeat this step as many times as required to specify the other v er tices of the polygon. 3. T o compl[...]

20060601 2-8 Drawing and Editing Objects Selecting and Deselecting Objects Before y ou can edit (move or delete) an object or create a fi gure using an object, y ou fi rst need to select par t of it or all of it. This section explains how to select and deselect objects. u T o select a par ticular object 1. If any tool icon is in the upper right c[...]

20060601 2-9 Drawing and Editing Objects 2. Mov e the pointer close to the object you want to select. • This will cause  marks to appear on some par t (ver tex, side , etc.) of the object. 3. Press x or perform the f ollowing operation: 2 (Edit) – 4:Select Figure. • This selects the entire object. u T o deselect a par ticular object 1. If [...]

20060601 2-10 Drawing and Editing Objects Using the Construct Menu Press 4 (Construct) to display the Construct menu. Y ou can use the Construct menu to construct various types of geometric objects, such as a per pendicular bisector , parallel, angle bisector , etc. u T o construct a perpendicular bisector 1. Draw a line segment and select it. 2. P[...]

20060601 2-11 Drawing and Editing Objects Note Y ou can perform a perpendicular constr uct operation while a single line segment and single point, a single line and single point, a single ra y and a single point, a single vector and a single point, or one side of a polygon and a single point are selected on the screen. u T o construct a midpoint 1.[...]

20060601 2-12 Drawing and Editing Objects u T o construct an angle bisector 1. Draw a triangle and select two of its sides . 2. P erform the follo wing operation: 4 (Construct) – 5:Angle Bisector. • This draws the bisector of the angle f or med by the two sides of the triangle that y ou selected. Note • Y ou can perf or m an angle bisector co[...]

20060601 2-13 Drawing and Editing Objects 2. P erform the follo wing operation: 4 (Construct) – 6:Parallel. • This will draw a par allel to the selected line segment that passes through the selected point. Note Y ou can perform a parallel construct operation while any of the f ollowing combination objects is selected. • A single line segment [...]

20060601 2-14 Drawing and Editing Objects Using the T ransform Menu Press 5 (T ransform) to display the T ransf orm menu. Y ou can use the T ransf or m menu to perform various transf or m operations, such as object refl ection, object rotation, etc. u T o refl ect an object 1. Draw the object y ou want to refl ect. Here, we will use a triangle. [...]

20060601 2-15 Drawing and Editing Objects Note • Y ou can specify a line segment, line, r ay , or one side of a polygon as the axis of refl ection. • If you select only part of an object before perf or ming step 3 of the above procedure , only the selected par t will be refl ected. If you selected side BC of the triangle in step 2, perform th[...]

20060601 2-16 Drawing and Editing Objects 4. After the values are the w ay you w ant, press w . • This performs parallel translation of the object b y the distance specifi ed by the v alues you input in step 3. Note If you select only part of an object before perf or ming step 2 of the above procedure , only the selected par t will be translated[...]

20060601 2-17 Drawing and Editing Objects 4. Press w . • This will perform parallel translation of the original object in the direction of the vector you selected. Note If you select only part of an object before perf or ming step 2 of the above procedure , only the selected par t will be translated. u T o rotate an object 1. Draw the object y ou[...]

20060601 2-18 Drawing and Editing Objects 5. Input the angle of rotation (counterclockwise) in degrees and then press w . • This will draw the original object, rotated the specifi ed amount. Note If you select only part of an object before perf or ming step 2 of the above procedure , only the selected par t will be rotated. u T o dilate an objec[...]

20060601 2-19 Drawing and Editing Objects 5. Input a scale value in the r ange of 0.1 < | x | < 10 and then press w . • This will draw a resiz ed version of the original object. Note • If you select only part of an object before perf or ming step 2 of the above procedure , only the selected par t will be dilated. • The f ollowing fi gu[...]

20060601 2-20 Drawing and Editing Objects Moving and Deleting an Object Before y ou can move or delete an object, y ou fi rst need to select it. For details , see “Selecting and Deselecting Objects” (page 2-8). u T o move an object Note Sometimes you ma y fi nd that an object will not mov e the way y ou want it to . If this happens , try lock[...]

20060601 2-21 Drawing and Editing Objects 4. T o move the object to the current location of the rectangle , press w . One vertex selected One side selected Three sides selected Note If you press v when nothing is selected on the screen, the pointer will change to a 4 , which you can use to pan (shift) the entire screen. u T o delete an object 1. Se[...]

20060601 2-22 Drawing and Editing Objects Hiding and Showing Objects Use the follo wing operations to hide specifi c objects and to sho w all currently hidden objects. u T o hide an object 1. Select the object you w ant to hide. 2. P erform the follo wing operation: K (Option) – 6:Hide. • This hides the selected objects. u T o show all hidden [...]

20060601 3-1 Controlling the Appearance of the Geometry Windo w 3. Controlling the Appearance of the Geometry Window This section provides inf or mation about how to control the appearance of the screen b y scrolling or zooming, and b y showing or hiding ax es and the grid. Displaying Ax es and the Grid Use the follo wing procedures to tur n displa[...]

20060601 3-2 Controlling the Appearance of the Geometry Windo w u T o toggle integer grid display on and off 1. Press !m (SET UP) to display the Setup screen. 2. Use c to mov e the highlighting to “Integer Grid”. 3. Use the follo wing key operations to select the setting y ou want. T o select this setting: Press this key: Integer grid on 1 (On)[...]

20060601 3-3 Controlling the Appearance of the Geometry Windo w u T o confi gure View Window settings 1. P erform the follo wing operation to displa y the Vie w Window screen: !3 (V -WIN). 2. Input values f or Xmin, Xmax, and Ymid. • If you w ant to return these settings to their initial defaults, press 1 (INIT). 3. After all the settings are th[...]

20060601 3-4 Controlling the Appearance of the Geometry Windo w 4. T o exit the P an mode, press J . Note In the P an mode, each press of w toggles the shape of the pointer between 2 and I . While the 2 pointer is display ed, you can use the cursor ke ys to move it to another location on the screen. Pressing the cursor ke ys while the I pointer is [...]

20060601 3-5 Controlling the Appearance of the Geometry Windo w 3. Mov e the pointer in the direction of the opposite edges of the zoom box area. • As you do , the calculator will display a selection boundary that will expand as y ou move the pointer . 4. After selecting the zoom bo x area you want, press w . • The area within the zoom bo x are[...]

20060601 4-1 Using T e xt and Labels in a Screen Image 4. Using T ext and Labels in a Screen Ima g e Y ou can use the procedures in this section to inser t text into a screen image . Y ou can also edit the labels that the calculator inser ts automatically for objects , and add labels to objects. Inserting T ext into Screen Images Y ou can use the f[...]

20060601 4-2 Using T e xt and Labels in a Screen Image u T o edit screen text 1. Select the text y ou want to edit. 2. Press J . • This displays the measurement bo x at the bottom of the screen. 3. Press w . • This displays the te xt input dialog box. 4. Edit the text and then press w . • This causes the newly edited te xt to appear on the sc[...]

20060601 4-3 Using T e xt and Labels in a Screen Image 2. Press J . • This displays the measurement bo x at the bottom of the screen. 3. Press d to highlight the up arrow b utton on the left side of the measurement box and then press w . • This displays an icon palette . 4. Use the cursor ke ys to move the highlighting to the < icon on the i[...]

20060601 4-4 Using T e xt and Labels in a Screen Image u T o add a new label 1. Select the side of the triangle to which you want to add the label. 2. Press J to display the measurement bo x. 3. Press d to highlight the up arrow b utton on the left side of the measurement box and then press w . • This displays an icon palette . 4. Use the cursor [...]

20060601 5-1 Using the Measurement Box 5. Using the Measurement Box Pressing J displays a measurement bo x at the bottom of the screen as shown below . Measurement Box Y ou can use the measurement box to perf or m the f ollowing operations . View the measurements of an object Displaying the measurement bo x and selecting an object displays combinat[...]

20060601 5-2 Using the Measurement Box The follo wing table describes the information that appears when you highlight each icon, and explains when each icon is a vailable f or selection. Icon Icon Name This icon appears when this is selected: Highlighting this icon displays: Lockable 5 Coordinates A single point Coordinates of the point Y es = Dist[...]

20060601 5-3 Using the Measurement Box Icon Icon Name This icon appears when this is selected: Highlighting this icon displays: Lockable : Rotation angle T wo points created by the 5 – 4:Rotation command Angle of rotation No ; Scale of dilation T wo points created by the 5 – 5:Dilation command Scale of dilation No < Label/T ext A point that [...]

20060601 5-4 Using the Measurement Box 4. Select the icons on the icon palette to display other measurements . • In the case of the line segment, for e xample, you can vie w its length, slope, and equation. Slope Equation 5. T o close the measurement box, press J twice. u T o display the area of a rectangular area Y ou can use the measurement box[...]

20060601 20070101 5-5 Using the Measurement Box 4. T o make the dra wing screen active , press J . • This causes the measurement box to become unhighlighted and the pointer to reappear on the drawing screen. 5. Press o to deselect the current points and then select points A, D , and C. • This causes the area of the triangle ADC to appear in the[...]

20060601 5-6 Using the Measurement Box Specifying a Measurement of an Object In the follo wing examples, w e specify the angle of a triangle and the length of one side of a triangle. u T o specify the angle of a triangle 1. Draw a triangle. 2. Select side AC and then select side BC . 3. Press J to display the measurement bo x. • This displays the[...]

20060601 5-7 Using the Measurement Box u T o specify the length of one side of a triangle Note • Specifying any one of the f ollowing measurements for the fi rst time in the fi le y ou are editing (or immediately after an all clear operation: 2 (Edit) – 6:Clear All) will cause the resulting object to be resized so it fi ts within the displa [...]

20060601 5-8 Using the Measurement Box 5. Press !m (SET UP) to display the Setup screen. 6. Press 3 (SCALE). 7. Press J to close the Setup screen. 8. Draw a triangle. 9. Select side AC . 10. Press J to display the measurement bo x. • This displays the length of side A C in the measurement box. 11. Input the value y ou want to specify for side A C[...]

20060601 5-9 Using the Measurement Box 12. Press w . • This changes the length of size A C to 120 and resizes the entire triangle accordingly . • View Window settings are update automatically so the resized triangle can fi t on the screen. Note that the scale values on the ax es also change. 13. Now input 90 as the length of side A C and then [...]

20060601 5-10 Using the Measurement Box u T o lock a particular measurement Y ou can lock a particular measurement by perf orming any one of the follo wing operations. • P erform the procedure under “Specifying a Measurement of an Object” (page 5-6) to specify the measurement. This will cause the specifi ed measurement to become lock ed auto[...]

20060601 5-11 Using the Measurement Box u T o unlock all objects on the screen P erform the follo wing operation: K (Option) – 4:Clr Constraint. This unlocks all loc ked settings. Note The abov e operation unlocks both measurements you loc ked manually , as well as objects that are lock ed automatically whenever the y are drawn. For e xample, the[...]

20060601 5-12 Using the Measurement Box 3. Press e to highlight the up arrow b utton on the right side of the measurement box and then press w . • This will display a men u. 4. Use f to mov e the highlighting to [Paste] and then press w . • This will cause the measurement in the measurement box to be pasted into the screen image. At this time, [...]

20060601 5-13 Using the Measurement Box u T o edit a measurement type tag 1. Select the measurement whose type tag you w ant to edit and then press J . • This will display the measurement bo x and display the type tag of the selected measurement inside it. 2. Press w . • This will display the label edit dialog bo x. 3. Input up to 14 characters[...]

20060601 5-14 Using the Measurement Box u T o display the result of a calculation that uses on-screen measurement values Example: With line segment AB and line segment CD (point C being on AB) drawn on the display as sho wn here, calculate the sum of ∠ ACD and ∠ DCB, and displa y the result on the screen. (54.72 + 125.28 = 180.00) • F or info[...]

20060601 5-15 Using the Measurement Box Note When a measurement is a coordinate or vector component, the label f or mat becomes, “@1X”, “@1Y”, etc. “@1X” indicates the x -value of a coordinate or the x -component value of a vector , while “@1Y” indicates the y -value of a coordinate or the y -component value of a vector . Specifying[...]

20060601 6-1 Working with Animations 6. W orking with Animations An animation consists of one or more point/curve pairs, in which the curve can be a line segment, circle, or arc. Y ou build an animation b y selecting a point/cur ve pair and then adding it to an animation. Creating and Running an Animation u T o add an animation and run it Example: [...]

20060601 6-2 Working with Animations Note • Y ou can repeat the abov e procedure to create multiple points that mov e simultaneously . T r y this: - Draw a line segment and plot another point. - Select the line segment and the point. - Repeat steps 2 and 3 abov e. Notice that both animations go at the same time! • T o star t a new animation, pe[...]

20060601 6-3 Working with Animations 6. Input 90 into the measurement box b y pressing ja w . • This makes the angle between line segments AB and DE 90 deg rees, and loc ks it. 7. Press Jo to deselect all objects on the screen. 8. Select line segments DE and DC, and then press J . 9. Press d w to display the icon palette , move the highlighting t[...]

20060601 6-4 Working with Animations 14. P erform the following oper ation: 6 (Animate) – 3:T race. • This specifi es point D (the one you selected in step 13) as the “trace point”. 15. P erform the following oper ation: 6 (Animate) – 5:Go (once). • This should cause a parabola to be traced on the displa y . Note that line segment AB i[...]

20060601 6-5 Working with Animations When you want to do this: Perf orm this procedure: Specify the number of steps to be used as point E trav els along line segment AB 1. Use c and f to move the highlighting on the Edit Animations screen to “Steps” and then press 1 (Step). 2. On the dialog box that appears, input an integer from 2 through 100 [...]

20060601 6-6 Working with Animations When you want to do this: Perf orm this procedure: Delete the animation assigned to point E 1. Use c and f to move the highlighting on the Edit Animations screen to “E”, which is located under “Animations”. 2. Press 1 (DEL). • This deletes the animation assigned to point E and causes “E” (along wit[...]

20060601 6-7 Working with Animations Generating an Animation T able Under default settings , an animation causes a specifi ed point to mov e along a specifi ed line segment, circle, or arc in 20 steps. Y ou can confi gure the calculator to generate a tab le, called an “animation tab le”, which records the coordinates of each step, the length[...]

20060601 6-8 Working with Animations 5. Press e to highlight the up arrow b utton on the right side of the measurement box and then press w . • This will display a men u. 6. Use f to mov e the highlighting to [Add T able] and then press w . • This will display an animation tab le that shows the length of line segment CD at each step of the anim[...]

20060601 6-9 Working with Animations 12. T o exit the animation table screen, press J . 13. T o close the measurement box, press J twice. Note • Y ou can add up to 26 columns to the animation table . • In place of steps 4 through 6 in the abov e procedure, you can use either of the f ollowing operations to add a column to the animation table: 6[...]

20060601 6-10 Working with Animations 2. Press 1 (ST O) 2 (S-SHT). • This displays a dialog bo x for inputting the spreadsheet fi le name . 3. Input up to 8 characters f or the fi le name and then press w . • For details about spreadsheet data, see “Chapter 9 Spreadsheet” in the man ual that comes with the calculator . u T o delete a par [...]

20060601 7-1 Error Messages 7. Error Messages Attempting to perform some inappropriate operation in the Geometry Mode will cause one of the error messages described below to appear . Use this table as a reference to fi nd out what you need to do when an error message appears . When you see this message: It means this: So you need to do this: First[...]

20060601 7-2 Error Messages When you see this message: It means this: So you need to do this: Range ERROR View Window settings are wrong. Confi gure proper settings or initialize View Window settings by pressing 1 (INIT) J . The Edit Animations screen is confi gured with the setting t0=t1. Confi gure the Edit Animations screen so t0 and t1 are a[...]

20060601 7-3 Error Messages When you see this message: It means this: So you need to do this: Select the applicable measurement icon. Y ou are trying to execute the Add T able command without fi rst selecting the appropriate measurement icon. Select the icon of a measurement that can be added to an animation table . First confi gure animation set[...]

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