E For fx-9860G Series/ GRAPH 95/75+/75/85 Series/ fx-9860GIII /fx-9750GIII/GRAPH35+ E II Geometry Application User’s Guide CASIO Worldwide Education Website https://edu.casio.
Contents Contents 1 2 3 4 5 6 7 Geometry Mode Overview Drawing and Editing Objects Controlling the Appearance of the Geometry Window Using Text and Labels in a Screen Image Using the Measurement Box Working with Animations Error Messages 20060601
1-1 Geometry Mode Overview 1. Geometry Mode Overview The Geometry Mode allows you to draw and analyze geometric objects. You can draw a triangle and specify values to change the size of its sides so they are 3:4:5, and then check the measurement of each of its angles. You can also lock the coordinates of a point or the length of a line segment, and you can draw a circle and then draw a line that is tangent to a particular point on the circle.
1-2 Geometry Mode Overview I C(View) To do this: Select this menu item: Start a box zoom operation 1:Zoom Box Enter the pan mode (page 3-3) 2:Pan Enter the scroll mode (page 3-4) 3:Scroll Enlarge the display image 4:Zoom In Reduce the size of the display image 5:Zoom Out Adjust the size of the display image so it fills the display 6:Zoom to Fit I (Edit) To do this: Select this menu item: Undo or redo the last operation 1:Undo/Redo Select all objects on the screen 2:Select All Deselect
1-3 Geometry Mode Overview I (Construct) To construct this: Select this menu item: A perpendicular bisector 1:Perp Bisector A perpendicular 2:Perpendicular A midpoint 3:Midpoint An intersection 4:Intersection An angle bisector 5:Angle Bisector A parallel 6:Parallel A tangent 7:Tangent I (Transform) To do this: Select this menu item: Reflect an object 1:Reflection Translate an object by specified values 2:Translation Translate an object using an existing vector 3:Trans(Sel Vec) Rot
1-4 Geometry Mode Overview I *(Option) To do this: Select this menu item: Input text 1:Text Input an expression 2:Expression Specify the number format Geometry 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 Pointer You can use the following operations to move the on-screen pointer (( ) around the display when drawing objects, editing objects, etc.
1-5 Geometry Mode Overview Using Key Help Pressing (File) – 4:Key Help or the ? key will display Key Help, which provides information the function of each key in the Geometry Mode. Use the A and D keys to navigate between the three Key Help screens. To exit the Key Help screens, press ). Note The key operations shown on the Key Help screens apply to the drawing screen only. Managing Geometry Mode Files This section explains how to save Geometry Mode data to files, and how to manage your files.
1-6 Geometry Mode Overview S To open an existing file 1. Perform the following operation: (File) – 2:Open. • This displays a menu of existing files. 2. Use A and D to move the highlighting to the file you want to open and then press U. • The following dialog box will appear if you have a drawing on the screen. 3. To clear the current drawing, press (Yes). • This will open the file you selected in step 2. S To delete a file 1. Perform the following operation: (File) – 2:Open.
1-7 Geometry Mode Overview S To save a file under a different name 1. While the file you want to save is open, perform the following operation: (File) – 3:Save as. • This will display the file name input screen and automatically switch the calculator’s keys to Alpha Lock. The cursor changes to when the keyboard is in Alpha Lock. 2. Input up to 8 characters for the file name and then press U. • You can use the following characters in a file name.
1-8 Geometry Mode Overview Key Functions The figure below shows the keys that are used for Geometry Mode drawing screen operations. Displays the measurement box. (Page 5-1) Displays menus. (Page 1-1) Moves the pointer. Cancels an operation, or returns to the previous menu or screen. Selects, deselects, executes. Selects an object to move it. (Page 2-20) Selects, deselects, executes. Selects an entire polygon. (Valid for polygons only.) (Page 2-8) Deletes the currently selected object.
2-1 Drawing and Editing Objects 2. Drawing and Editing Objects This section explains how to perform the following operations. • Plot points, draw line segments, polygons, etc. ([F3](Draw) [F3](Draw) (Draw) menu) • Select and deselect objects ([F2](Edit) [F2](Edit) (Edit) menu) • For a drawn object, construct a perpendicular bisector, perpendicular, etc.
2-2 Drawing and Editing Objects S To add a labeled point to an existing line Note You can use the following procedure to add a labeled point to an existing line, to a side of a polygon, to the periphery of a circle, etc. 1. Perform the following operation: (Draw) – 1:Point. 2. Move the pointer on the screen towards the line where you want to add the labeled point. • This selects the line, which is indicated by “I”. “ / 3. Press U. • This will add a point on the line at the pointer location.
2-3 Drawing and Editing Objects S To draw an infinite line 1. Perform the following operation: (Draw) – 3:Infinite Line. 2. Move the pointer to any location on the display and then press U. 3. Move the pointer to another location on the display and then press U. • This will draw a line that passes between the two points. S To drew a ray 1. Perform the following operation: (Draw) – 4:Ray. 2. Move the pointer to any location on the display and then press U. 3.
2-4 Drawing and Editing Objects S To draw a circle 1. Perform the following operation: (Draw) – 6:Circle. 2. Move the pointer to the location on the display where you want the center point of the circle to be and then press U. 3. Move the pointer to the location on the display where you want the circumference of the circle to be and then press U. • This draws a circle whose center point is the point you specified in step 2 and whose circumference runs through the point you specified in step 3.
2-5 Drawing and Editing Objects S To draw a triangle 1. Perform the following operation: (Draw) – 8:Triangle. 2. Move the pointer to any location on the display and then press U. 3. Move the pointer to another location. • This causes a selection boundary to appear, indicating the size of the triangle that will be drawn. 4. Press U. • This draws a triangle.
2-6 Drawing and Editing Objects S To draw an isosceles triangle 1. Perform the following operation: (Draw) – 9:Isosc Triangle. 2. Perform steps 2 through 4 under “To draw a triangle” (page 2-5). • This draws an isosceles triangle. S To draw a rectangle or a square 1. Perform either of the following operations: (Draw) – A:Rectangle or (Draw) – B:Square. 2. Move the pointer to any location on the display and then press U. • This causes a cross ( ) ( to appear at the pointer location. 3.
2-7 Drawing and Editing Objects S To draw a polygon 1. Perform the following operation: (Draw) – C:Polygon. 2. Move the pointer to the location on the display where you want a vertex of the polygon to be and then press U. • Repeat this step as many times as required to specify the other vertices of the polygon. 3. To complete the polygon, move the pointer to the location of the first vertex and then press U.
2-8 Drawing and Editing Objects Selecting and Deselecting Objects Before you can edit (move or delete) an object or create a figure using an object, you first need to select part of it or all of it. This section explains how to select and deselect objects. S To select a particular object 1. If any tool icon is in the upper right corner of the screen, press ) or M to deselect the tool. 2. Move the pointer close to the object you want to select. • This will cause one or more : marks to appear on the object.
2-9 Drawing and Editing Objects 2. Move the pointer close to the object you want to select. • This will cause : marks to appear on some part (vertex, side, etc.) of the object. 3. Press V or perform the following operation: (Edit) – 4:Select Figure. • This selects the entire object. S To deselect a particular object 1. If any tool icon is in the upper right corner of the screen, press ) or M to deselect the tool. 2. Move the pointer close to the object you want to deselect.
2-10 Drawing and Editing Objects Using the Construct Menu Press (Construct) to display the Construct menu. You can use the Construct menu to construct various types of geometric objects, such as a perpendicular bisector, parallel, angle bisector, etc. S To construct a perpendicular bisector 1. Draw a line segment and select it. 2. Perform the following operation: (Construct) – 1:Perp Bisector. • This will draw the perpendicular bisector of the line segment you selected.
2-11 Drawing and Editing Objects Note You can perform a perpendicular construct operation while a single line segment and single point, a single line and single point, a single ray 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. S To construct a midpoint 1. Draw a line segment and select it. 2. Perform the following operation: (Construct) – 3:Midpoint. • This will plot the midpoint of the line segment you selected.
2-12 Drawing and Editing Objects S To construct an angle bisector 1. Draw a triangle and select two of its sides. 2. Perform the following operation: (Construct) – 5:Angle Bisector. • This draws the bisector of the angle formed by the two sides of the triangle that you selected.
2-13 Drawing and Editing Objects 2. Perform the following operation: (Construct) – 6:Parallel. • This will draw a parallel to the selected line segment that passes through the selected point. Note You can perform a parallel construct operation while any of the following combination objects is selected.
2-14 Drawing and Editing Objects Using the Transform Menu Press (Transform) to display the Transform menu. You can use the Transform menu to perform various transform operations, such as object reflection, object rotation, etc. S To reflect an object 1. Draw the object you want to reflect. Here, we will use a triangle. 2. Draw a line segment that represents the axis of the reflection. 3. Perform the following operation: (Transform) – 1:Reflection. • This will cause the message “Select Axis” to appear.
2-15 Drawing and Editing Objects Note • You can specify a line segment, line, ray, or one side of a polygon as the axis of reflection. • If you select only part of an object before performing step 3 of the above procedure, only the selected part will be reflected. If you selected side BC of the triangle in step 2, perform the rest of the steps starting from step 3 would reflect side BC only as shown below. / S To translate an object by specified values 1. Draw the object you want to translate.
2-16 Drawing and Editing Objects 4. After the values are the way you want, press U. • This performs parallel translation of the object by the distance specified by the values you input in step 3. Note If you select only part of an object before performing step 2 of the above procedure, only the selected part will be translated. S To translate an object using an existing vector 1. Draw the object you want to translate. Here, we will use a triangle.
2-17 Drawing and Editing Objects 4. Press U. • 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 performing step 2 of the above procedure, only the selected part will be translated. S To rotate an object 1. Draw the object you want to rotate. Here, we will use a triangle. 2. Perform the following operation: (Transform) – 4:Rotation. • This will cause the message “Sel Rotation Center” to appear. 3.
2-18 Drawing and Editing Objects 5. Input the angle of rotation (counterclockwise) in degrees and then press U. • This will draw the original object, rotated the specified amount. / Note If you select only part of an object before performing step 2 of the above procedure, only the selected part will be rotated. S To dilate an object 1. Draw the object you want to dilate. Here, we will use a triangle. 2. Perform the following operation: (Transform) – 5:Dilation.
2-19 Drawing and Editing Objects 5. Input a scale value in the range of 0.1 | x | 10 and then press U. • This will draw a resized version of the original object. / Note • If you select only part of an object before performing step 2 of the above procedure, only the selected part will be dilated. • The following figure illustrates the meanings of the terms used in the above procedure. Center of Dilation Scale: –1 Scale: 0.
2-20 Drawing and Editing Objects Moving and Deleting an Object Before you can move or delete an object, you first need to select it. For details, see “Selecting and Deselecting Objects” (page 2-8). S To move an object Note Sometimes you may find that an object will not move the way you want it to. If this happens, try locking the part(s) of the object that you do not want to move (page 5-10), or temporarily unlock all objects (Clr Constraint, page 5-11). 1. Select the object you want to move.
2-21 Drawing and Editing Objects 4. To move the object to the current location of the rectangle, press U. One vertex selected One side selected Three sides selected Note If you press T when nothing is selected on the screen, the pointer will change to a , which you can use to pan (shift) the entire screen. / / S To delete an object 1. Select the object you want to delete. • If you want to delete only one of the vertices of a triangle for example, select the vertex.
2-22 Drawing and Editing Objects Hiding and Showing Objects Use the following operations to hide specific objects and to show all currently hidden objects. S To hide an object 1. Select the object you want to hide. 2. Perform the following operation: *(Option) – 6:Hide. • This hides the selected objects. S To show all hidden objects Perform the following operation: *(Option) – 5:Show All. This shows all currently hidden objects.
3-1 Controlling the Appearance of the Geometry Window 3. Controlling the Appearance of the Geometry Window This section provides information about how to control the appearance of the screen by scrolling or zooming, and by showing or hiding axes and the grid. Displaying Axes and the Grid Use the following procedures to turn display of the axes and grid on or off. S To specify the axis setting 1. Press K(SET UP) to display the Setup screen. 2.
3-2 Controlling the Appearance of the Geometry Window S To toggle integer grid display on and off 1. Press K(SET UP) to display the Setup screen. 2. Use A to move the highlighting to “Integer Grid”. 3. Use the following key operations to select the setting you want. To select this setting: Press this key: Integer grid on (On) Integer grid off (Off) 4. After the setting is the way you want, press ).
3-3 Controlling the Appearance of the Geometry Window S To configure View Window settings 1. Perform the following operation to display the View Window screen: (V-WIN). 2. Input values for Xmin, Xmax, and Ymid. • If you want to return these settings to their initial defaults, press (INIT). 3. After all the settings are the way you want, press ). Using Pan and Scroll to Shift the Display Image There are two methods available for shifting the contents of the screen.
3-4 Controlling the Appearance of the Geometry Window 4. To exit the Pan mode, press ). Note In the Pan mode, each press of U toggles the shape of the pointer between and . While the pointer is displayed, you can use the cursor keys to move it to another location on the screen. Pressing the cursor keys while the pointer is displayed will shift (pan) the screen contents. S To scroll the screen 1. Press or perform the following operation: C(View) – 3:Scroll.
3-5 Controlling the Appearance of the Geometry Window 3. Move 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 you move the pointer. 4. After selecting the zoom box area you want, press U. • The area within the zoom box area expands to fill the entire screen. S To zoom in and out To double the size of the displayed image, press C(View) – 4:Zoom In.
4-1 Using Text and Labels in a Screen Image 4. Using Text and Labels in a Screen Image You can use the procedures in this section to insert text into a screen image. You can also edit the labels that the calculator inserts automatically for objects, and add labels to objects. Inserting Text into Screen Images You can use the following procedure to insert text into a screen image and to edit existing text. S To insert text into a screen image 1.
4-2 Using Text and Labels in a Screen Image S To edit screen text 1. Select the text you want to edit. 2. Press ). • This displays the measurement box at the bottom of the screen. 3. Press U. • This displays the text input dialog box. 4. Edit the text and then press U. • This causes the newly edited text to appear on the screen. / 5. To close the measurement box, press ) twice. Adding or Modifying a Label Label operations are explained in this section using a triangle.
4-3 Using Text and Labels in a Screen Image 2. Press ). • This displays the measurement box at the bottom of the screen. 3. Press B to highlight the up arrow button on the left side of the measurement box and then press U. • This displays an icon palette. 4. Use the cursor keys to move the highlighting to the press U. icon on the icon palette and then 5. Press C to move the highlighting back to the measurement box and then press U.
4-4 Using Text and Labels in a Screen Image S To add a new label 1. Select the side of the triangle to which you want to add the label. 2. Press ) to display the measurement box. 3. Press B to highlight the up arrow button on the left side of the measurement box and then press U. • This displays an icon palette. 4. Use the cursor keys to move the highlighting to the press U. icon on the icon palette and then 5. Press C to move the highlighting back to the measurement box and then press U.
5-1 Using the Measurement Box 5. Using the Measurement Box Pressing ) displays a measurement box at the bottom of the screen as shown below. Measurement Box You can use the measurement box to perform the following operations.
5-2 Using the Measurement Box The following table describes the information that appears when you highlight each icon, and explains when each icon is available for selection.
5-3 Using the Measurement Box Icon Icon Name This icon appears when this is selected: Highlighting this icon displays: Rotation angle Two points created by the – 4:Rotation command Angle of rotation No Scale of dilation Two points created by the – 5:Dilation command Scale of dilation No Label/Text A point that has a label or an object that can be named Label text No Lockable You can use the measurement box to determine certain measurements.
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 example, you can view its length, slope, and equation. Slope Equation 5. To close the measurement box, press ) twice. S To display the area of a rectangular area You can use the measurement box to display the area of a triangle formed by any three points you select on the display.
5-5 Using the Measurement Box 4. To make the drawing screen active, press ). • This causes the measurement box to become unhighlighted and the pointer to reappear on the drawing screen. 5. Press M 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 measurement box. The above procedure shows that the areas of the two triangles are the same. 6. To close the measurement box, press ).
5-6 Using the Measurement Box Specifying a Measurement of an Object In the following examples, we specify the angle of a triangle and the length of one side of a triangle. S To specify the angle of a triangle 1. Draw a triangle. 2. Select side AC and then select side BC. 3. Press ) to display the measurement box. • This displays the size of ACB (in degrees) in the measurement box. 4. Input the value you want to specify for ACB (in degrees) into the measurement box and then press U.
5-7 Using the Measurement Box S To specify the length of one side of a triangle Note • Specifying any one of the following measurements for the first time in the file you are editing (or immediately after an all clear operation: (Edit) – 6:Clear All) will cause the resulting object to be resized so it fits within the display area.
5-8 Using the Measurement Box 5. Press K(SET UP) to display the Setup screen. 6. Press (SCALE). 7. Press ) to close the Setup screen. 8. Draw a triangle. 9. Select side AC. 10. Press ) to display the measurement box. • This displays the length of side AC in the measurement box. 11. Input the value you want to specify for side AC into the measurement box. • Here, we will input 120.
5-9 Using the Measurement Box 12. Press U. • This changes the length of size AC to 120 and resizes the entire triangle accordingly. • View Window settings are update automatically so the resized triangle can fit on the screen. Note that the scale values on the axes also change. 13. Now input 90 as the length of side AC and then press U. • Using A as the point of reference, side AC is resized to 90. In this case, the length of side AC is shortened, without altering the overall size of the triangle.
5-10 Using the Measurement Box S To lock a particular measurement You can lock a particular measurement by performing any one of the following operations. • Perform the procedure under “Specifying a Measurement of an Object” (page 5-6) to specify the measurement. This will cause the specified measurement to become locked automatically. / • If the icon to the right of the measurement box is !, move the highlighting to the icon and press U.
5-11 Using the Measurement Box S To unlock all objects on the screen Perform the following operation: *(Option) – 4:Clr Constraint. This unlocks all locked settings. Note The above operation unlocks both measurements you locked manually, as well as objects that are locked automatically whenever they are drawn. For example, the above operation unlocks all of the following lock conditions.
5-12 Using the Measurement Box 3. Press C to highlight the up arrow button on the right side of the measurement box and then press U. • This will display a menu. 4. Use D to move the highlighting to [Paste] and then press U. • This will cause the measurement in the measurement box to be pasted into the screen image. At this time, the pasted measurement text is selected. / 5. Move the text to another location on the screen, if you want.
5-13 Using the Measurement Box S To edit a measurement type tag 1. Select the measurement whose type tag you want to edit and then press ). • This will display the measurement box and display the type tag of the selected measurement inside it. 2. Press U. • This will display the label edit dialog box. 3. Input up to 14 characters for the label type tag. • To delete the label type tag, press M. 4. Press U. • This changes the measurement, which is highlighted on the display. 5.
5-14 Using the Measurement Box S To 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 shown here, calculate the sum of ACD and DCB, and display the result on the screen. (54.72 + 125.28 = 180.00) • For information about displaying measurement values of ACD and DCB, see “Pasting Measurements into a Screen Image” (page 5-11). 1.
5-15 Using the Measurement Box Note When a measurement is a coordinate or vector component, the label format 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 the Number Format of a Measurement You can specify the number format for each measurement on the screen. Note The initial default number format is “Norm 1”.
6-1 Working with Animations 6. Working with Animations An animation consists of one or more point/curve pairs, in which the curve can be a line segment, circle, or arc. You build an animation by selecting a point/curve pair and then adding it to an animation. Creating and Running an Animation S To add an animation and run it Example: To animate a point around a circle 1. Plot a point and draw a circle, and select them. 2. Perform the following operation: (Animate) – 1:Add Animation.
6-2 Working with Animations Note • You can repeat the above procedure to create multiple points that move simultaneously. Try this: - Draw a line segment and plot another point. - Select the line segment and the point. - Repeat steps 2 and 3 above. Notice that both animations go at the same time! • To start a new animation, perform the procedure under “To replace the current animation with a new one” below. S To replace the current animation with a new one 1.
6-3 Working with Animations 6. Input 90 into the measurement box by pressing H?U. • This makes the angle between line segments AB and DE 90 degrees, and locks it. 7. Press )M to deselect all objects on the screen. 8. Select line segments DE and DC, and then press ). 9. Press BU to display the icon palette, move the highlighting to the press U. w / 10. Use C to move the highlighting to the ! icon and then press U. • This changes the icon to . • This makes line segments DE and DC congruent in length.
6-4 Working with Animations 14. Perform the following operation: (Animate) – 3:Trace. • This specifies point D (the one you selected in step 13) as the “trace point”. 15. Perform the following operation: (Animate) – 5:Go (once). • This should cause a parabola to be traced on the display. Note that line segment AB is the directrix and point C is the focus of the parabola.
6-5 Working with Animations When you want to do this: Specify the number of steps to be used as point E travels along line segment AB Perform this procedure: 1. Use A and D to move the highlighting on the Edit Animations screen to “Steps” and then press (Step). / 2. On the dialog box that appears, input an integer from 2 through 100 and then press U. Specify the start point and the end point of the movement of point E along line segment AB 1.
6-6 Working with Animations When you want to do this: Delete the animation assigned to point E Perform this procedure: 1. Use A and D to move the highlighting on the Edit Animations screen to “E”, which is located under “Animations”. 2. Press (DEL). • This deletes the animation assigned to point E and causes “E” (along with the “t0” and “t1” values under it) to disappear from under “Animations” screen.
6-7 Working with Animations Generating an Animation Table Under default settings, an animation causes a specified point to move along a specified line segment, circle, or arc in 20 steps. You can configure the calculator to generate a table, called an “animation table”, which records the coordinates of each step, the length of the line segment, the area of the object, etc.
6-8 Working with Animations 5. Press C to highlight the up arrow button on the right side of the measurement box and then press U. • This will display a menu. 6. Use D to move the highlighting to [Add Table] and then press U. • This will display an animation table that shows the length of line segment CD at each step of the animation in a column labeled “Length”. 7. Press ) to close the animation table screen. 8. Press ) again to make the drawing screen active. 9.
6-9 Working with Animations 12. To exit the animation table screen, press ). 13. To close the measurement box, press ) twice. Note • You can add up to 26 columns to the animation table. • In place of steps 4 through 6 in the above procedure, you can use either of the following operations to add a column to the animation table: (Animate) – 7:Add Table or @.
6-10 Working with Animations 2. Press (STO) (S-SHT). • This displays a dialog box for inputting the spreadsheet file name. 3. Input up to 8 characters for the file name and then press U. • For details about spreadsheet data, see “Chapter 9 Spreadsheet” in the manual that comes with the calculator. S To delete a particular column from an animation table 1. Display the animation table. 2. Use B and C to move the highlighting to the column you want to delete. 3. Press (DEL) (DEL).
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 find 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 select a segment. You are attempting to construct a perpendicular bisector without first selecting a line segment. Select the required object(s) and then try again.
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. Configure proper settings or initialize View Window settings by pressing (INIT)). The Edit Animations screen is configured with the setting t0=t1. Configure the Edit Animations screen so t0 and t1 are assigned different values for the same animation. Too Many Animations You are trying to add more than 10 animations.
7-3 Error Messages When you see this message: It means this: So you need to do this: Select the applicable measurement icon. You are trying to execute the Add Table command without first selecting the appropriate measurement icon. Select the icon of a measurement that can be added to an animation table. First configure animation settings and create a table. You tried to execute the Display Table command without generating an animation table. Generate an animation table first.
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