Casio Geometry User manual

http://edu.casio.com
Add-in application for fx-9860G series/ E
GRAPH 85 series calculators
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 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. 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 define.
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 eand dto move between menu screens.
• To close a menu without selecting anything, press J.
kMenu 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 3to display the Draw menu, use cand fto highlight “5:Vector”, and then
press w.
• Press 3to 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.
k1(File)
To do this: Select this menu item:
Create a new file 1:New
Open a file 2:Open
Save a file 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
k1e(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
k2(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
k3(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:Infinite 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
k4(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
k5(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)
Rotate an object 4:Rotation
Dilate an object 5:Dilation
k6(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 2:Replace Anima
Turn on trace for a point and trace the movement of the point
while animation is being executed 3:Trace
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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Geometry Mode Overview
kK(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.
uTo 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.
uTo make the pointer jump to a particular location
Pressing a number key (bto j) will cause the pointer to jump to the corresponding
section of the screen as shown below.
hij
efg
bcd

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1-5
Geometry Mode Overview
Using Key Help
Pressing 1(File) – 4:Key Help or the akey will display Key Help, which provides
information the function of each key in the Geometry Mode.
Use the cand fkeys 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 files, and how to manage your
files.
Note
Whenever you save a file 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.
uTo create a new file
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 file, press 1(Yes).
• This will create a new file and display a blank drawing screen.

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Geometry Mode Overview
uTo open an existing file
1. Perform the following operation: 1(File) – 2:Open.
• This displays a menu of existing files.
2. Use cand fto move the highlighting to the file 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 file you selected in step 2.
uTo delete a file
1. Perform the following operation: 1(File) – 2:Open.
• This displays a menu of existing files.
2. Use cand fto move the highlighting to the file you want to delete and then press
1(DEL).
• This causes a confirmation dialog box to appear.
3. Press 1(Yes) to delete the selected file or 6(No) to cancel the delete operation.
4. To exit the file menu, press J.

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Geometry Mode Overview
uTo save a file under a different name
1. While the file you want to save is open, perform the following operation: 1(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
0when the
keyboard is in Alpha Lock.
2. Input up to 8 characters for the file name and then press w.
• You can use the following characters in a file name.
-Uppercase alphabetic characters A through Z
-Lower-case rand Greek letter
θ
-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 wto save the file and return to its drawing
screen.

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Geometry Mode Overview
Key Functions
The figure below shows the keys that are used for Geometry Mode drawing screen
operations.
Displays menus.
(Page 1-1)
Selects an entire polygon.
(Valid for polygons only.)
(Page 2-8)
Displays Key Help.
(Page 1-5)
Selects, deselects,
executes.
Selects, deselects,
executes.
Zooms in/out.
(Page 3-5)
Undoes/Redoes an
operation.
(Page 2-19)
Moves the pointer.
Selects, deselects,
executes.
Selects an object to
move it. (Page 2-20)
!bAdds an
animation table.
(Page 6-7)
Causes the pointer to
jump to a particular
position. (Page 1-4)
Enters the Scroll
mode. (Page 3-4)
Zooms the screen
image to fit the
window area.
(Page 3-5)
Displays the
measurement box.
(Page 5-1)
Cancels an operation,
or returns to the
previous menu or
screen.
Deletes the currently
selected object.
(Page 2-21)
Deselects all, cancels
an operation, deletes
all (when pressed
twice).
Displays menus.
(Page 1-1)
Selects an entire polygon.
(Valid for polygons only.)
(Page 2-8)
Displays Key Help.
(Page 1-5)
Selects, deselects,
executes.
Selects, deselects,
executes.
Zooms in/out.
(Page 3-5)
Undoes/Redoes an
operation.
(Page 2-19)
Moves the pointer.
Selects, deselects,
executes.
Selects an object to
move it. (Page 2-20)
!bAdds an
animation table.
(Page 6-7)
Causes the pointer to
jump to a particular
position. (Page 1-4)
Enters the Scroll
mode. (Page 3-4)
Zooms the screen
image to fit the
window area.
(Page 3-5)
Displays the
measurement box.
(Page 5-1)
Cancels an operation,
or returns to the
previous menu or
screen.
Deletes the currently
selected object.
(Page 2-21)
Deselects all, cancels
an operation, deletes
all (when pressed
twice).
20070101

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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) 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.
uTo 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 Jicon will remain on the display, which means you repeat step 2 to plot more
points, if you want.
3. After you are finished plotting all the points you want, press oor Jto deselect the
Point tool.
Note
Some drawing tools remain after you draw something, like the Point tool. To deselect such a
tool, press oor J.

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Drawing and Editing Objects
uTo 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.
uTo 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
uTo draw an infinite line
1. Perform the following operation: 3(Draw) – 3:Infinite 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.
uTo 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 first point you selected and that passes through
the second point.
uTo 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
uTo 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 specified in step 2 and whose
circumference runs through the point you specified 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.
uTo 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
uTo 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 wis very close to the point you specified
in step 2, the triangle that is drawn will be the maximum size that fits 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 fits in the screen if the
second point specified is too close to or at the same location of the first point.
Example: When drawing a triangle
//

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Drawing and Editing Objects
uTo 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.
uTo 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 wis very close to the point you specified
in step 2, the object that is drawn will be the maximum size that fits 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
uTo 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 first vertex and then
press w.
Note
If you press Jin place of step 3, the figure will be finalized as-is, resulting in an unclosed
non-polygon.
uTo 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 specified in step 2.

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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.
uTo select a particular object
1. If any tool icon is in the upper right corner of the screen, press Jor oto 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.
(Line Segment)
(Point)
(Circle)
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.
uTo select an entire polygon
1. If any tool icon is in the upper right corner of the screen, press Jor oto 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 xor perform the following operation: 2(Edit) – 4:Select Figure.
• This selects the entire object.
uTo deselect a particular object
1. If any tool icon is in the upper right corner of the screen, press Jor oto deselect the
tool.
2. Move the pointer close to the object you want to deselect.
• This will cause the kmark(s) to become highlighted.
3. Press w.
• This will deselect the object, which causes the kmark(s) to disappear.
uTo select all objects on the screen
Perform the following operation: 2(Edit) – 2:Select All.
uTo deselect all objects on the screen
Press oor perform the following operation: 2(Edit) – 3:Deselect All.
//

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Drawing and Editing Objects
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.
uTo 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.
uTo 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.