Key Curriculum Press TITANIUM TI-89 User manual

77,,77,,33OOXXVV99RR\\DDJJHH
77KHKH**HHRRPPHHWWHHUUVV66NNHHWWFFKKSSDGDGë
Getting Started
Introductory Tour Customer Support
Advanced Tour
Using the Tools
Selection Arrow Straightedge Tools
Point Tool Text Tool
Compass Tool Custom Tool
Using the Menus
Edit Transform
Display Measure
Construct Graph
Tips and Techniques
Shortcuts Construction Hints
Display Hints Performance Tips
..HH\\&&XXUUUULLFXFXOOXXPP33UUHHVVVVë
Innovators in Mathematics Education
ti

..HH\\&&XXUUUULLFFXXOOXXPP33UUHHVVVVë
Innovators in Mathematics Education
THE
GEOMETER·S
SKETCHPAD®
for TI-89
TI-92 Plus
VoyageTM 200
User Guide and
Reference Manual

The Geometer’s Sketchpad®forTI-89,
TI-92 Plus, andVoyage™ 200 PLT
Version 1.0
Project Design: Nicholas Jackiw
Program Implementation: Keith Dean, Nicholas Jackiw, Scott Steketee
Documentation: Dan Bennett, Steven Chanan, Nicholas Jackiw,
Tom Reich
Special Thanks: Laura Harvey, Zach Teitler, Julio Valella
Product Information: http://www.keypress.com/sketchpad/ti
The Geometer’s Sketchpad is the product of a collaboration between the
Visual Geometry Project at Swarthmore College and Key Curriculum
Press. The Visual Geometry Project was directed by Dr. Eugene Klotz and
Dr. Doris Schattschneider. Portions of this material are based upon work
supported by the National Science Foundation under award DMI-9996103.
Any opinions, findings, and conclusions or recommendations expressed in
this publication are those of the authors and do not necessarily reflect the
views of the National Science Foundation.
The Geometer’s Sketchpad and Dynamic Geometry are registered
trademarks of Key Curriculum Press, Inc. Sketchpad is a trademark of
Key Curriculum Press, Inc. All other brand names and product names are
trademarks or registered trademarks of their respective holders.
Copyright © 2000-2002 by KCP Technologies, Inc. All rights reserved.
KCP Technologies, Inc.
1150 65th Street
Emeryville, CA 94608
The Geometer’s Sketchpad for TI-89,TI-92 Plus, and Voyage™ 200 PLT
is distributed by
Texas Instruments U.S.A.
7800 Banner Drive
Dallas, Texas 75251
TI Support and Service Information
For General Information
E-mail: ti-[email protected]
Phone: 1-800-TI-CARES (1-800-842-2737)
For U.S., Canada, Mexico, Puerto Rico, and Virgin
Islands only
Home Page: education.ti.com
For Technical Questions
Phone: [phone]
For Product (hardware) Service
Customers in the U.S., Canada, Mexico, Puerto Rico and Virgin
Islands: Always contact Texas Instruments Customer Support before
returning a product for service.
All other customers: Refer to the leaflet enclosed with this product
(hardware) or contact your local Texas Instruments retailer/distributor.

Contents
Dynamic Geometry®....................................................................................5
Introductory Tour.........................................................................................6
Advanced Tour ..........................................................................................13
Where to Go from Here.............................................................................17
Using Tools................................................................................................22
Selection Arrow Tools...............................................................................24
Point Tool ..................................................................................................27
Compass Tool............................................................................................28
Straightedge Tools.....................................................................................30
Text Tool ...................................................................................................31
Custom Tool ..............................................................................................34
Using Menus..............................................................................................40
ƒEdit Menu ............................................................................................42
„Display Menu.......................................................................................53
…Construct Menu ...................................................................................58
† Transform Menu..................................................................................63
‡ Measure Menu .....................................................................................69
ˆ Graph Menu.........................................................................................74
Shortcuts....................................................................................................81
Construction and Display Hints.................................................................84
Performance Tips.......................................................................................86
88
1 Introducing Sketchpad
2 Tools
3 Commands
4 Tips and Techniques
Index

The Geometer’s Sketchpad®for TI-89, TI-92 Plus, and © 2000-2002 KCP Technologies,Inc.4
Voyage™ 200 PLT User Guide and Reference Manual
Introducing Sketchpad
1
For new users of The Geometer’s Sketchpad forTI-89,TI-92 Plus, and
Voyage™ 200 PLT, this chapter offers a brief introduction to
Sketchpad and Dynamic Geometry. Two tutorials, called Guided
Tours, will give you experience with many of Sketchpad’s features.
The chapter ends with an overview of the rest of this User Guide.
A cube in two-point perspective. While Sketchpad is two-
dimensional in nature, you can use it to build mathematical
models of higher-dimensional geometry “projected” into two
dimensions. This sketch demonstrates a two-point perspective
view of a (three-dimensional) cube. In this perspective, vertical
edges of the 3-D cube remain vertical in its 2-D image, but other
edges recede toward one of two vanishing points on the
image’s horizon line. Dragging the vanishing points alters the
perspective dynamically. (Example from a TI-89.)
The circumcircle of a triangle. This sketch
starts with a triangle ABC. Construct the
midpoints of each side, and then construct
side bisectors—lines perpendicular to each
side passing through that side’s midpoint.
The three bisectors concur in a single
point. This point, the circumcenter of the
triangle, is the center of the unique circle
which passes through all of the triangle’s
vertices. In what sort of situations does a
triangle’s circumcenter fall outside of that
triangle? (Example from a TI-92 Plus.)

The Geometer’s Sketchpad®for TI-89, TI-92 Plus, and © 2000-2002 KCP Technologies,Inc.5
Voyage™ 200 PLT User Guide and Reference Manual
The Geometer’s Sketchpad for TI-89,TI-92 Plus, and Voyage™200 PLT
is a powerful tool for learning concepts from geometry, algebra, and other
math subjects. Geometric relationships can be hard to visualize from the
static, unchanging figures in a text, or even from figures you draw yourself
with traditional tools like a compass, ruler, and protractor. With Sketchpad,
you can construct and measure figures easily and more precisely than with
traditional tools. But more importantly, Sketchpad’s Dynamic Geometry
lets you move parts of your constructions to see which properties change
and which don’t. With Dynamic Geometry at your fingertips you can put
the problems and theorems you encounter in your math class in motion,
revealing relationships and giving you a whole new way of seeing
mathematics.
Try the following two Guided Tours for an overview of Dynamic
Geometry and how to use Sketchpad on your TI-89 or TI-92 Plus
/Voyage 200 PLT. Or explore on your own, and turn to the reference
sections if you need help learning how to do something.
This manual assumes that Sketchpad has already been installed as a Flash
application on your handheld device. Detailed Flash application
installation instructions are available from education.ti.com/guides.
Dynamic Geometry®
This section gives a brief introduction to The Geometer’s
Sketchpad and to the significance of Dynamic Geometry.
Installing Sketchpad

The Geometer’s Sketchpad®for TI-89, TI-92 Plus, and © 2000-2002 KCP Technologies,Inc.6
Voyage™ 200 PLT User Guide and Reference Manual
With Sketchpad’s drawing tools and menus, you can construct figures that
are very flexible, so that you can drag any parts of them wherever and
however you want; or you can construct them with properties that limit
how you can change them. In this tour, you’ll draw a triangle that can be
any size or shape. Then you’ll construct an isosceles triangle, which is
constrained so that two sides are always equal. You’ll also discover some
other properties of isosceles triangles. In the process, you’ll learn some of
the basics of using Sketchpad’s drawing tools, as well as the ƒEdit,
„Display, …Construct, and ‡Measure menus.
Follow the steps below to construct a general triangle.
Steps
Display
1. Press Oand select [The
Geometer’s] Sketchpad to open
Sketchpad. You’ll see a blank
Sketchpad sketch, with
Sketchpad’s menus (ƒ–ˆ)
along the top of the screen and
the toolbox (Š) along the right
edge.
2. Press Š(TI-89: 2 Š) to
enter the toolbox. Then press @
until the Segment tool blinks.
(The Segment tool appears at
the left of three pop-up
Straightedge tools.) Press ¸
to choose it. Once the Segment
tool is active, the cursor
becomes a cross-hair.
3. Press ¸to construct a
segment endpoint. Press @to
move away from the first
endpoint, constructing a
segment as you move. Press
¸again to construct the
segment’s second endpoint.
4. Construct the first of two more segments to complete the triangle.
With the cursor still positioned on the endpoint of your first segment,
construct a second segment by pressing ¸, @to drag away, and
¸again to complete the second segment.
Introductory Tour
This is the first of two Guided Tours, which are geometric
investigations with step-by-step instructions designed to
introduce you to many of Sketchpad’s features.
Drawing
The square brackets in the
instructions at right mean
that text this appears as
Sketchpad on the TI-89
and as The Geometer’s
Sketchpad on the
TI-92 Plus/Voyage™ 200
PLT.
The @symbol refers to the
large multidirectional cursor
pad on the TI-92 Plus and to
the four cursor keys on the
TI-89.
The Straightedge tools are
used for making segments,
rays, and lines. When you
choose one, it remains
active until you choose a
different tool or arrow.
On the TI-89,you can use
Minstead of ¸ for
easier keyboard entry when
using tools or selecting
objects.

The Geometer’s Sketchpad®for TI-89, TI-92 Plus, and © 2000-2002 KCP Technologies,Inc.7
Voyage™ 200 PLT User Guide and Reference Manual
5. With the cursor still positioned
on the endpoint of your second
segment, press ¸, @back
to the original endpoint, and
¸to construct the third
segment. Be sure this segment
connects back to the starting
point before you press the final
¸that completes the
triangle.
You can drag parts of your triangle to change its size and shape.
Steps
Display
1. Press Nto quit the Segment
tool and choose the Arrow tool.
2. Position the Arrow over a
vertex. (The cursor changes to a
sideways arrow when it points
to an object.) Press and hold ‚
(TI-89: j), then press @to
drag the vertex. Drag it around
the entire screen.
3. Practice dragging the other
vertices of the triangle. Try
dragging a side, too. Notice how
you can make this triangle any
size or shape.
Dragging is at the heart of Dynamic Geometry. It lets you generalize from
a single construction. For example, in the steps above, you drew a single
triangle. But by dragging, you can look at many possible sizes and shapes
for a triangle. You can also drag to check that your construction is holding
together properly—that all possible appearances are still triangles. Drag
often!
Sketchpad’s unlimited undo lets you look back at a previous state of your
sketch. You can also use undo if you need to correct a construction
mistake.
Steps
Display
1. Press ƒEdit: ¨Undo to
undo the last step. Repeat to
undo a few more steps.
The Edit menu (TI-92 Plus
/Voyage™ 200 PLT)
2. Press ƒEdit: ©Redo to redo the steps you’ve just undone.
Throughout these tours, use undo (and redo) to revisit your work, or
to correct any mistakes you make while constructing objects.
You might notice a
“snapping” action when the
cursor gets close to an
existing point.
Dragging
Nserves many purposes
in Sketchpad—one of which
is a shortcut for the Arrow
tool. (You can also choose
the Arrow by pressing
[TI-89: 2]Š.)
Undoing
Every menu has a name,
represented by an icon on
the screen. The ƒmenu is
the Edit menu.

The Geometer’s Sketchpad®for TI-89, TI-92 Plus, and © 2000-2002 KCP Technologies,Inc.8
Voyage™ 200 PLT User Guide and Reference Manual
You can save your work in case you want to return to it later, after you’ve
worked on something else.
Steps
Display
1. Press ƒEdit: oSketch:
ªSave to save the sketch.
Sketchpad presents a dialog box
that lets you specify a folder and
a variable name.
2. To save this sketch in the main
folder, press Dto move the
cursor into the Variable field
and type triang1. Then press
¸twice to save.
Congratulations! You’ve constructed your first geometric figure with
Sketchpad: a triangle.
In this part of the investigation, you’ll construct an isosceles triangle and
investigate some of its properties.
Steps
Display
1. Press ƒEdit: oSketch:
¨New to open a new sketch.
The sketch area becomes blank
again.
2. Press Š(TI-89: 2 Š), Dto
the Segment tool, and press
¸to choose the Segment
tool. Then press ¸@
¸to construct a segment.
3. Press Š(TI-89: 2 Š) D
until the Compass tool blinks,
then press ¸to choose it.
4. To construct a circle with this
segment as radius, move the
Compass tool’s cursor to one
segment endpoint, press ¸.
Then press @to start drawing a
circle. Position the cursor over
the second segment endpoint
and press ¸to finish your
circle there.
Saving
Constructing
A shortcut for activating the
segment tool is ¥†
(TI-89 : ¥y). (There are
comparable shortcuts for
each of the other tools in the
Toolbox based on position.
For example, the Point tool
is the second tool down, so
its shortcut is ¥„
[TI-89: ¥©].)
This is tricky! Be sure you
start your circle on one
segment endpoint and finish
it with the cursor directly
over the second segment
endpoint. Otherwise, the
circle and segment will not
be connected. Look for the
snapping action when the
cursor gets close to the
point you want.

The Geometer’s Sketchpad®for TI-89, TI-92 Plus, and © 2000-2002 KCP Technologies,Inc.9
Voyage™ 200 PLT User Guide and Reference Manual
5. Press Nto return to the
Arrow, then press and hold ‚
(TI-89:j) while using @to
drag the circle’s two defining
points to be sure the circle and
segment are connected.
6. Use the Segment tool to draw
another radius of the circle. Be
sure to place one endpoint with
the cursor positioned at the
circle’s center (¸) and the
other endpoint with the cursor
anywhere on the circle’s
circumference (¸).
7. Construct a segment to connect
the two points on the circle and
complete the triangle.
8. Press Nto return to the
Arrow. Then position it on a
vertex, press and hold ‚
(TI-89 : j), and press @to
drag the vertex. Drag the other
vertices too, and observe how
each changes the triangle.
Did you notice that two sides of this triangle always appear to stay equal?
Why? Did you notice that dragging one of the vertices didn’t change the
length of these equal sides? What’s different about that point?
You can automate dragging using animation. Follow these steps to animate
one vertex traveling around the circle.
Steps
Display
1. Press Nto deselect all
objects. Press ¸on the
point on the circle that does not
change the circle’s radius to
select it. If you’re not sure you
have the right point, drag it first.
2. Press „Display: nAnimate
Point.
3. To stop the animation, Press „Display: (TI-89: j) ÑStop
Animation.
There should be only two
points in your sketch that
define both the segment and
the circle. If the circle
separates from the segment
when you drag, undo (ƒ
¨)until the circle is gone
and try again.
Remember: On the TI-89,
you can use Mas a
shortcut for ¸when
drawing or selecting objects.
(The Mkey might be
easier to reach.)
Animating
You’ve probably noticed that
pressing ¸with the
Arrow over an object
changes the object’s
appearance to indicate
you’ve selected it. In
general, you need to select
objects that you want to act
upon with menu commands.