# Casio Geometry User Manual

E
GRAPH 85 series calculators
Geometry
User's Guide
http://edu.casio.com

#### Summary of Contents for Casio Geometry

• Page 1 Add-in application for fx-9860G series/ GRAPH 85 series calculators Geometry User’s Guide http://edu.casio.com...

Contents 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 Contents 20060601...
• ### Page 3: 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.
• Page 4 Draw a circle Draw an arc Draw a triangle Draw an isosceles triangle Draw a rectangle Draw a square Draw a polygon Draw a regular n-gon Geometry Mode Overview 20060601 Select this menu item: 1:Zoom Box 2:Pan 3:Scroll 4:Zoom In 5:Zoom Out...
• Page 5 Display the animation editing screen Perform an animation sequence once Perform an animation sequence repeatedly Add one or more values to the animation table (page 6-7) Display the animation table Geometry Mode Overview 20060601 Select this menu item: 1:Perp Bisector 2:Perpendicular...
• Page 6 K(Option) To do this: Input text Input an expression Specify the number format Geometry Mode measurements Unlock all measurements Display all objects Hide the currently selected object Using the Pointer You can use the following operations to move the on-screen pointer ( 2) around the display when drawing objects, editing objects, etc.
• Page 7 ﬁ les. Note Whenever you save a ﬁ le in the Geometry Mode, it is stored in main memory in a folder named “<@GEOM>”. You can use the calculator’s MEMORY mode to view the data in main memory. For more information, see the manual that comes with your calculator.
• Page 8 1(DEL). • This causes a conﬁ rmation dialog box to appear. 3. Press 1(Yes) to delete the selected ﬁ le or 6(No) to cancel the delete operation. 4. To exit the ﬁ le menu, press J. Geometry Mode Overview 20060601...
• Page 9 1. While the ﬁ le you want to save is open, perform the following operation: 1(File) – 3:Save as. • This will display the ﬁ le name input screen and automatically switch the calculator’s keys to Alpha Lock. The cursor changes to 0 when the 2.
• ### Page 10: Key Functions

Key Functions The ﬁ gure below shows the keys that are used for Geometry Mode drawing screen operations. Displays menus. Displays menus. (Page 1-1) (Page 1-1) Selects, deselects, Selects, deselects, executes. executes. Selects an object to Selects an object to move it.
• ### Page 11: 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) menu) • Select and deselect objects ([F2](Edit) menu) • For a drawn object, construct a perpendicular bisector, perpendicular, etc. ([F4](Construct) menu) •...
• Page 12 Drawing and Editing Objects u 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.
• Page 13 Drawing and Editing Objects u To draw an inﬁ nite line 1. Perform the following operation: 3(Draw) – 3:Inﬁ nite Line. 2. Move the pointer to any location on the display and then press w. 3. Move the pointer to another location on the display and then press w. •...
• Page 14 Drawing and Editing Objects u To draw a circle 1. Perform the following operation: 3(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 w. 3.
• Page 15 Drawing and Editing Objects u To draw a triangle 1. Perform the following operation: 3(Draw) – 8:Triangle. 2. Move the pointer to any location on the display and then press w. 3. Move the pointer to another location. • This causes a selection boundary to appear, indicating the size of the triangle that will be drawn.
• Page 16 Drawing and Editing Objects u To draw an isosceles triangle 1. Perform the following operation: 3(Draw) – 9:Isosc Triangle. 2. Perform steps 2 through 4 under “To draw a triangle” (page 2-5). • This draws an isosceles triangle. u To draw a rectangle or a square 1.
• Page 17 Drawing and Editing Objects u To draw a polygon 1. Perform the following operation: 3(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 w. •...
• Page 18 Selecting and Deselecting Objects Before you can edit (move or delete) an object or create a ﬁ gure using an object, you ﬁ rst need to select part of it or all of it. This section explains how to select and deselect objects. u To select a particular object 1.
• Page 19 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 x or perform the following operation: 2(Edit) – 4:Select Figure. •...
• Page 20 Using the Construct Menu Press 4(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. u To construct a perpendicular bisector 1. Draw a line segment and select it. 2.
• Page 21 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. u To construct a midpoint 1.
• Page 22 Drawing and Editing Objects u To construct an angle bisector 1. Draw a triangle and select two of its sides. 2. Perform the following operation: 4(Construct) – 5:Angle Bisector. • This draws the bisector of the angle formed by the two sides of the triangle that you selected.
• Page 23 Drawing and Editing Objects 2. Perform the following operation: 4(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.
• Page 24 Using the Transform Menu Press 5(Transform) to display the Transform menu. You can use the Transform menu to perform various transform operations, such as object reﬂ ection, object rotation, etc. u To reﬂ ect an object 1. Draw the object you want to reﬂ ect. Here, we will use a triangle. 2.
• Page 25 Drawing and Editing Objects Note • You can specify a line segment, line, ray, or one side of a polygon as the axis of reﬂ ection. • If you select only part of an object before performing step 3 of the above procedure, only the selected part will be reﬂ...
• Page 26 Drawing and Editing Objects 4. After the values are the way you want, press w. • This performs parallel translation of the object by the distance speciﬁ ed 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.
• Page 27 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 performing step 2 of the above procedure, only the selected part will be translated.
• Page 28 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 performing step 2 of the above procedure, only the selected part will be rotated.
• Page 29 2-19 Drawing and Editing Objects 5. Input a scale value in the range of 0.1 < | | < 10 and then press w. • 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.
• Page 30 Moving and Deleting an Object Before you can move or delete an object, you ﬁ rst need to select it. For details, see “Selecting and Deselecting Objects” (page 2-8). u To move an object Note Sometimes you may ﬁ nd 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).
• Page 31 Drawing and Editing Objects 4. To move the object to the current location of the rectangle, press w. One vertex 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.
• Page 32 2-22 Drawing and Editing Objects Hiding and Showing Objects Use the following operations to hide speciﬁ c objects and to show all currently hidden objects. u To hide an object 1. Select the object you want to hide. 2. Perform the following operation: K(Option) – 6:Hide. •...
• ### Page 33: Controlling The Appearance Of The Geometry Window

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.
• Page 34 Controlling the Appearance of the Geometry Window u To toggle integer grid display on and off 1. Press !m(SET UP) to display the Setup screen. 2. Use c to move the highlighting to “Integer Grid”. 3. Use the following key operations to select the setting you want.
• Page 35 Controlling the Appearance of the Geometry Window u To conﬁ gure View Window settings 1. Perform the following operation to display the View Window screen: !3(V-WIN). 2. Input values for Xmin, Xmax, and Ymid. • If you want to return these settings to their initial defaults, press 1(INIT).
• Page 36 3. To exit the Scroll mode, press J. Zooming The Geometry Mode provides you with a selection of zoom commands that you can use to enlarge or reduce an entire screen image or a speciﬁ c area of an object.
• Page 37 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.
• ### Page 38: Using Text And Labels In A Screen Image

1. Move the pointer to the location on the screen where you want to insert the text. 2. Perform the following operation: K(Option) – 1:Text. • This will display a text input dialog box and automatically switch the calculator’s keys to Alpha Lock.
• Page 39 Using Text and Labels in a Screen Image u To edit screen text 1. Select the text you want to edit. 2. Press J. • This displays the measurement box at the bottom of the screen. 3. Press w. • This displays the text input dialog box. 4.
• Page 40 5. Press e to move the highlighting back to the measurement box and then press w. • This will display a label editing dialog box and automatically switch the calculator’s keys to Alpha Lock. 6. Input up to 14 characters for the label text and then press w.
• Page 41 Using Text and Labels in a Screen Image u To 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 box. 3. Press d to highlight the up arrow button on the left side of the measurement box and then press w.
• ### Page 42: Using The Measurement Box

5. Using the Measurement Box Pressing J displays a measurement box at the bottom of the screen as shown below. You can use the measurement box to perform the following operations. View the measurements of an object Displaying the measurement box and selecting an object displays combinations of the following measurements, depending on the type of object you select: coordinates, distance/ length, slope, equation, vector, radius, circumference, perimeter, area, angle, supplementary angle, tangency, congruence, incidence, or point on curve.
• Page 43 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. This icon appears Icon Icon Name when this is selected: Coordinates A single point Two points on one object Distance/ or two different objects,...
• Page 44 Using the Measurement Box This icon appears Icon Icon Name when this is selected: Two points created by the 5 – 4:Rotation Rotation angle command Two points created by Scale of the 5 – 5:Dilation dilation command A point that has a label <...
• Page 45 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. 5. To close the measurement box, press J twice. u 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.
• Page 46 Using the Measurement Box 4. To make the drawing 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. •...
• Page 47 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. u To specify the angle of a triangle 1. Draw a triangle. 2. Select side AC and then select side BC. 3.
• Page 48 Using the Measurement Box u To specify the length of one side of a triangle Note • Specifying any one of the following measurements for the ﬁ rst time in the ﬁ le you 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...
• Page 49 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 box. • This displays the length of side AC in the measurement box. 11.
• Page 50 12. Press w. • 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 ﬁ t on the screen. Note that the scale values on the axes also change. 13.
• Page 51 Using the Measurement Box u 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 speciﬁ ed measurement to become locked automatically.
• Page 52 u To unlock all objects on the screen Perform the following operation: K(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.
• Page 53 3. Press e to highlight the up arrow button on the right side of the measurement box and then press w. • This will display a menu. 4. Use f to move the highlighting to [Paste] and then press w. •...
• Page 54 u To edit a measurement type tag 1. Select the measurement whose type tag you want to edit and then press J. • This will display the measurement box and display the type tag of the selected measurement inside it. 2.
• Page 55 Using the Measurement Box u 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.
• ### Page 56: Specifying The Number Format Of A Measurement

Note The initial default number format is “Norm 1”. For details about number formats, see “2-3 Specifying the Angle Unit and Display Format” in the manual that comes with the calculator. u To specify the number format of a measurement Example: To specify two decimal places for measurement values 1.
• ### Page 57: 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 u To add an animation and run it Example: To animate a point around a circle...
• Page 58 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! •...
• Page 59 6. Input 90 into the measurement box by pressing jaw. • This makes the angle between line segments AB and DE 90 degrees, and locks it. 7. Press Jo to deselect all objects on the screen. 8. Select line segments DE and DC, and then press J. 9.
• Page 60 • The calculator’s auto power off feature will turn off power if an animation is being performed. If calculator power is turned off (either by auto power off or manually) while an animation is being performed, the animation will be stopped.
• Page 61 Working with Animations When you want to do Perform this procedure: this: Specify the number of 1. Use c and f to move the highlighting on the Edit Animations screen to “Steps” and then press 1(Step). steps to be used as point E travels along line segment AB 2.
• Page 62 When you want to do Perform this procedure: this: Delete the animation 1. Use c and f to move the highlighting on the Edit assigned to point E 2. Press 1(DEL). Note Selecting “Animations” in step 1 and then pressing 1(DEL) will delete the animations assigned to all points.
• Page 63 Under default settings, an animation causes a speciﬁ ed point to move along a speciﬁ ed line segment, circle, or arc in 20 steps. You can conﬁ gure 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.
• Page 64 5. Press e to highlight the up arrow button on the right side of the measurement box and then press w. • This will display a menu. 6. Use f to move the highlighting to [Add Table] and then press w. •...
• Page 65 4. Input the list number as an integer from 1 to 26 and then press w. • For details about list data, see “Chapter 3 List Function” in the manual that comes with the calculator. u To save an entire animation table as spreadsheet data 1.
• Page 66 3. Input up to 8 characters for the ﬁ le name and then press w. • For details about spreadsheet data, see “Chapter 9 Spreadsheet” in the manual that comes with the calculator. u To delete a particular column from an animation table 1.
• ### Page 67: 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.
• Page 68 When you see It means this: this message: Range ERROR View Window settings are wrong. The Edit Animations screen is conﬁ gured with the setting t0=t1. Too Many You are trying to add more than Animations 10 animations. First select You are trying to execute the Trace point(s).
• Page 69 When you see It means this: this message: Select the You are trying to execute the applicable Add Table command without measurement ﬁ rst selecting the appropriate icon. measurement icon. First conﬁ gure You tried to execute the Display animation Table command without settings and generating an animation table.
• Page 70 CASIO COMPUTER CO., LTD. 6-2, Hon-machi 1-chome Shibuya-ku, Tokyo 151-8543, Japan SA0701-B...

#### This manual is also suitable for:

Fx-9680g seriesGraph 85 series