Casio Geometry User Manual

Add-in application for fx-9860G series/ GRAPH 85 series calculators

Geometry

User’s Guide

http://edu.casio.com

Contents

1 Geometry Mode Overview

2 Drawing and Editing Objects

3 Controlling the Appearance of the Geometry

Window

4 Using Text and Labels in a Screen Image

5 Using the Measurement Box

6 Working with Animations

7 Error Messages

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Geometry Mode Overview

1-1

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. The Geometry Mode also includes an animation feature that lets you watch how an object changes in accordance with conditions you deﬁ ne.

Geometry Mode Menus

Unlike other modes, the Geometry Mode does not have function menus along the bottom of the screen. Instead, it uses menus named [F1] through [F6] and [OPT], like the ones shown below.

The following is a general explanation of Geometry Mode menus.

• Pressing a key that corresponds to a menu ([F1] through [F6] or [OPT]) will display the menu for that tab.

• After displaying a menu, use e and d to move between menu screens.

• To close a menu without selecting anything, press J.

k Menu Operations in This Manual

This manual shows menu operations using the following form: 3(Draw) – 5:Vector. When you see this, it means you can perform either of the following two operations.

• Press 3 to display the Draw menu, use c and f to highlight “5:Vector”, and then press w.

• Press 3 to display the Draw menu and then press f.

Menu Reference

The following tables describe the menu items that appear on each of the Geometry Mode menus.

k 1(File)

To do this: Select this menu item:

Create a new ﬁ le 1:New

Open a ﬁ le 2:Open

Save a ﬁ le under a new name 3:Save as

Display a list of functions assigned to each key 4:Key Help

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Geometry Mode Overview

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k 1e(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 ﬁ lls the display 6:Zoom to Fit

k 2(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 all objects on the screen 3:Deselect All

Select an entire polygon (page 2-8) 4:Select Figure

Delete the currently selected object 5:Delete

Clear the screen 6:Clear All

k 3(Draw)

To do this: Select this menu item:

Plot a point 1:Point

Draw a line segment 2:Line Segment

Draw a straight line 3:Inﬁ nite Line

Draw a ray 4:Ray

Draw a vector 5:Vector

Draw a circle 6:Circle

Draw an arc 7:Arc

Draw a triangle 8:Triangle

Draw an isosceles triangle 9:Isosc Triangle

Draw a rectangle A:Rectangle

Draw a square B:Square

Draw a polygon C:Polygon

Draw a regular n-gon D:Regular n-gon

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Geometry Mode Overview

1-3

k 4(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

k 5(Transform)

To do this: Select this menu item:

Reﬂ ect an object 1:Reﬂ ection

Translate an object by speciﬁ ed values 2:Translation

Translate an object using an existing vector 3:Trans(Sel Vec)

Rotate an object 4:Rotation

Dilate an object 5:Dilation

k 6(Animate)

To do this: Select this menu item:

Add animation to two selected objects 1:Add Animation

Replace the current animation assigned to two selected objects

Turn on trace for a point and trace the movement of the point while animation is being executed

Display the animation editing screen 4:Edit Animation

Perform an animation sequence once 5:Go (once)

Perform an animation sequence repeatedly 6:Go (repeat)

Add one or more values to the animation table (page 6-7) 7:Add Table

Display the animation table 8:Display Table

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2:Replace Anima

3:Trace

Geometry Mode Overview

1-4

k K(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 ( 2) around the display when drawing objects, editing objects, etc.

u To move the pointer

Use the cursor keys to move the pointer around the display. Holding down a cursor key moves the pointer at high speed.

u To make the pointer jump to a particular location

Pressing a number key ( b to j) will cause the pointer to jump to the corresponding section of the screen as shown below.

hij

efg

bcd

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Geometry Mode Overview

1-5

Using Key Help

Pressing 1(File) – 4:Key Help or the a key will display Key Help, which provides information the function of each key in the Geometry Mode.

Use the c and f keys to navigate between the three Key Help screens.

To exit the Key Help screens, press J.

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 ﬁ les, and how to manage your 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.

u To create a new ﬁ le

1. Perform the following operation: 1(File) – 1:New.

• The following dialog box will appear if you have a drawing on the screen.

2. To clear the current drawing and create a new ﬁ le, press 1(Yes).

• This will create a new ﬁ le and display a blank drawing screen.

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Geometry Mode Overview

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u To open an existing ﬁ le

1. Perform the following operation: 1(File) – 2:Open.

• This displays a menu of existing ﬁ les.

2. Use c and f to move the highlighting to the ﬁ le you want to open and then press w.

• The following dialog box will appear if you have a drawing on the screen.

3. To clear the current drawing, press 1(Yes).

• This will open the ﬁ le you selected in step 2.

u To delete a ﬁ le

1. Perform the following operation: 1(File) – 2:Open.

• This displays a menu of existing ﬁ les.

2. Use c and f to move the highlighting to the ﬁ le you want to delete and then press

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.

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Geometry Mode Overview

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u To save a ﬁ le under a different name

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.

2. Input up to 8 characters for the ﬁ le name and then press w.

• You can use the following characters in a ﬁ le name.

- Uppercase alphabetic characters A through Z

- Lower-case

r and Greek letter

- Numerals 0 through 9

- Period (.), blank space, quotes ("), plus sign (+), minus sign (–), multiplication sign (×), division sign (÷), brackets ([ ]), braces ({ })

• After inputting the name you want, press w to save the ﬁ le and return to its drawing

screen.

The cursor changes to 0 when the

keyboard is in Alpha Lock.

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Geometry Mode Overview

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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 2-20)

move it. (Page 2-20)

Selects an entire polygon.

Selects an entire polygon. (Valid for polygons only.)

(Valid for polygons only.) (Page 2-8)

(Page 2-8)

!b Adds an

animation table.

animation table. (Page 6-7)

(Page 6-7)

Causes the pointer to

Causes the pointer to jump to a particular

jump to a particular position. (Page 1-4)

position. (Page 1-4)

Displays Key Help.

Displays Key Help. (Page 1-5)

(Page 1-5)

Enters the Scroll

Enters the Scroll mode. (Page 3-4)

mode. (Page 3-4)

Zooms the screen

Zooms the screen image to fit the

image to fit the window area.

window area. (Page 3-5)

(Page 3-5)

Displays the

Displays the measurement box.

measurement box. (Page 5-1)

(Page 5-1)

Moves the pointer.

Cancels an operation,

Cancels an operation, or returns to the

or returns to the previous menu or

previous menu or screen.

screen.

Selects, deselects,

Selects, deselects, executes.

executes.

Deletes the currently

Deletes the currently selected object.

selected object. (Page 2-21)

(Page 2-21)

Deselects all, cancels

Deselects all, cancels an operation, deletes

an operation, deletes all (when pressed

all (when pressed twice).

twice).

Undoes/Redoes an

Undoes/Redoes an operation.

operation. (Page 2-19)

(Page 2-19)

Zooms in/out.

Zooms in/out. (Page 3-5)

(Page 3-5)

Selects, deselects,

Selects, deselects, executes.

executes.

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20070101

Drawing and Editing Objects

2-1

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)

• For a drawn object, perform various transform operations ([F5](Transform) menu)

• Undo an operation, move an object, delete an object and other editing operations ([F2](Edit) menu)

Using the Draw Menu

Press 3(Draw) to display the Draw menu. You can use the Draw menu to plot points, and draw line segments, triangles, polygons, and other objects.

u To plot a point

1. Perform the following operation: 3(Draw) – 1:Point.

2. Move the pointer to the location on the screen where you want to plot a point and then

press w.

• This will plot a point at the pointer location.

• The J icon will remain on the display, which means you repeat step 2 to plot more

points, if you want.

3. After you are ﬁ nished plotting all the points you want, press o or J to deselect the

Point tool.

Note

Some drawing tools remain after you draw something, like the Point tool. To deselect such a tool, press o or J.

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Drawing and Editing Objects

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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. Perform the following operation: 3(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 “ □ ”.

3. Press w.

• This will add a point on the line at the pointer location.

u To draw a line segment

1. Perform the following operation: 3(Draw) – 2:Line Segment.

2. Move the pointer to the location on the display from where you want to draw the line

segment and then press w.

3. Move the pointer to the location on the display to where you want to draw the line

segment and then press w.

• This will draw a line segment between the two points.

Note

In steps 2 and 3 of the above procedure, you can move the pointer to an existing point on the screen and press w. This will make the existing point one of the ends of the line segment.

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Drawing and Editing Objects

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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.

• This will draw a line that passes between the two points.

u To drew a ray

1. Perform the following operation: 3(Draw) – 4:Ray.

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.

• This will draw a ray that starts from the ﬁ rst point you selected and that passes through

the second point.

u To draw a vector

1. Perform the following operation: 3(Draw) – 5:Vector.

2. Move the pointer to the location on the display from where you want to draw the vector

and then press w.

3. Move the pointer to the location on the display to where you want to draw the vector and

then press w.

• This draws the vector.

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Drawing and Editing Objects

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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. Move the pointer to the location on the display where you want the circumference of the

circle to be and then press w.

• This draws a circle whose center point is the point you speciﬁ ed in step 2 and whose

circumference runs through the point you speciﬁ ed in step 3. In other words, the distance between the two points you specify is the radius of the circle.

Note

In steps 2 and 3 of the above procedure, you can move the pointer to an existing point on the screen and press w. This will make the existing point either the center point or the circumference point.

u To draw an arc

1. Perform the following operation: 3(Draw) – 7:Arc.

2. Move the pointer to the location on the display where you want the center point of the arc

to be and then press w.

3. Move the pointer to the location on the display where you want the start point of the arc to

be and then press w.

4. Move the pointer to the location where you want the end point of the arc to be.

5. Move the pointer and the line segment to the location on the display where you want the

end point of the arc to be and then press w.

• An arc will be drawn from the start point to the end point, in a counterclockwise direction.

..........

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Drawing and Editing Objects

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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.

4. Press w.

• This draws a triangle.

• If the location of the pointer when you press w is very close to the point you speciﬁ ed

in step 2, the triangle that is drawn will be the maximum size that ﬁ ts in the screen.

Note

The same type of two-point selection boundary in the above procedure is also used when drawing an isosceles triangle, rectangle, square, or regular n-gon.

In each case, the resulting object will be the maximum size that ﬁ ts in the screen if the second point speciﬁ ed is too close to or at the same location of the ﬁ rst point.

Example: When drawing a triangle

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Drawing and Editing Objects

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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. Perform either of the following operations: 3(Draw) – A:Rectangle or 3(Draw) –

B:Square.

2. Move the pointer to any location on the display and then press w.

• This causes a cross ( 3) to appear at the pointer location.

3. Move the pointer to another location.

• This causes a selection boundary to appear, indicating the size of the rectangle (or

square) that will be drawn.

4. Press w.

• This draws a rectangle or square.

• If the location of the pointer when you press w is very close to the point you speciﬁ ed

in step 2, the object that is drawn will be the maximum size that ﬁ ts in the screen.

Note

In the case of a square, each side will be the length of the shorter side of the rectangle you specify with the selection boundary in step 3.

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Drawing and Editing Objects

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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.

• 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 ﬁ rst vertex and then

press w.

Note

If you press J in place of step 3, the ﬁ gure will be ﬁ nalized as-is, resulting in an unclosed non-polygon.

u To draw a regular n-gon

1. Perform the following operation: 3(Draw) – D:Regular n-gon.

• This displays a dialog box prompting you to specify the number of sides.

2. Input a value from 3 to 12 and then press w.

3. Perform steps 2 through 4 under “To draw a triangle” (page 2-5).

• This will draw a regular n-gon using the number of sides you speciﬁ ed in step 2.

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Drawing and Editing Objects

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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. If any tool icon is in the upper right corner of the screen, press J or o 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.

3. Press w.

• This will cause the  to change to k, which indicates that the object is selected.

• Now you can repeat steps 2 and 3 to select other objects, if you want.

(Line Segment)

(Point)

(Circle)

u To select an entire polygon

1. If any tool icon is in the upper right corner of the screen, press J or o to deselect the

tool.

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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.

• This selects the entire object.

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u To deselect a particular object

1. If any tool icon is in the upper right corner of the screen, press J or o to deselect the

tool.

2. Move the pointer close to the object you want to deselect.

• This will cause the k mark(s) to become highlighted.

3. Press w.

• This will deselect the object, which causes the k mark(s) to disappear.

u To select all objects on the screen

Perform the following operation: 2(Edit) – 2:Select All.

u To deselect all objects on the screen

Press o or perform the following operation: 2(Edit) – 3:Deselect All.

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Drawing and Editing Objects

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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. Perform the following operation: 4(Construct) – 1:Perp Bisector.

• This will draw the perpendicular bisector of the line segment you selected.

Note

You can perform a perpendicular bisector construct operation while a single line segment, one side of a polygon, or two points are selected on the screen.

u To construct a perpendicular

1. Draw a line segment, plot a point, and select the line and point.

2. Perform the following operation: 4(Construct) – 2:Perpendicular.

• This will draw a perpendicular to the selected line segment and passes through the

selected point.

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Drawing and Editing Objects

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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. Draw a line segment and select it.

2. Perform the following operation: 4(Construct) – 3:Midpoint.

• This will plot the midpoint of the line segment you selected.

Note

You can perform a midpoint construct operation while a single line segment, one side of a polygon, or two points are selected on the screen.

u To construct the point of intersection of two lines

1. Draw to intersecting line segments and select them.

2. Perform the following operation: 4(Construct) – 4:Intersection.

• This plots the point where the two line segments intersect.

Note

You can construct the point of intersection of two lines while two of any of the following objects (two of the same object or two different objects) are selected on the screen: line segment, line, rays, vector, side of a polygon, circle, or arc.

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