Interactive Geometry is a dynamic geometry platform that allows one to construct,
measure, manipulate, transform and animate geometric figures. There are three
ways to use the features of tool: select an entry of the Menubar, click on
a Toolbar icon, or type into the Command Window.
For example, three ways to Draw a Segment and Construct it's midpoint
- choose Draw | Segment then Construct | Midpoint;
- choose then ;
- choose Options | Command Window and type draw segment [[0,3][5,3]],
draw midpoint [[0,3][5,3]].
Interactive Geometry launches in a Coordinate environment. However,
you can turn off the grid, axes, and disable snap to grid to easily move
into a Synthetic environment, depending upon your needs.
See also Settings.
Drawing Geometric Objects
Select the desired toolbar icon or its corresponding Draw menu option to activate
a draw tool. Once a draw tool has been selected, the ability to draw that particular
object will remain active until you select a different tool button or menu
See also Draw Commands, and the Measure
and Calculate features.
Figure or Polygon
Click once for each vertex, then double-click to end.
Click once to place a new point; place a point on a drawn object once
Click and drag from first endpoint to second, or select two points.
Click and drag from first endpoint to second, or select two points.
Click and drag from one point on the line to another, or select two
Click and drag from one point on the line of the half plane to another,
or select two points.
Click and drag from center of circle to a point on the circle.
Click three times to define a point, vertex, and another point; angle
is determined counterclockwise from initial to final.
Click and drag from initial point to second point, or select two points.
There are two common ways to Select drawn objects: use the tool
(Shift click to select multiple), or choose Help | List of Shapes (Control
click to select multiple, close the window).
Once selected, objects can be moved by dragging. The style of selected objects
can also be changed.
See also Transformations, Settings.
Measure and Calculate
To measure a drawn object, first select an
object, then choose an attribute to be measured or calculated from the Measurements
menu. Double-click a measurement to modify the Calculation, Label, and see
the result within a Calculation window.
Each measurement option and the objects that can be measured using that command
are listed below:
- Coordinates: Gives the matrix representation of any object drawn in the
plane (defined by its points). Available within the Coordinate geometry environment
Note: All coordinate measurements will be represented by a matrix
of size 2 x ? with the first and second rows for the x- and y-coordinates,
respectively. Each column represents the coordinates of a single point.
The Style of an object(s) can be changed to show coordinates as ordered
- Lengths: Gives the absolute value of the distance between points defining
a segment, ray, line, half plane, circle, or angle.
- Angles: Gives the angle measure (in degrees) of an angle or all the angles
in a figure or polygon.
- Slopes: Gives the slope of the segment, ray, line, half plane, or the
segments defining a figure or polygon, or angle.
- Perimeter/Circumference: Gives the total distance around a figure or polygon,
collection of segments, or circle.
- Area: Gives the total space enclosed by a figure or polygon, or circle.
Choose Measurements | Calculation to perform
a calculation using numerical values, or previously-calculated results or measurements.
Within a Calculation window:
- Type the desired calculation (e.g., +, -, /, *); click on the drop-down
list to insert an existing measurement or result.
- Choose a label for the calculation (or leave it blank) and click the Test
button (this is what will display on the screen).
- Click OK to insert this labeled calculation into your drawing.
Select an object(s) and a construction option from the toolbar or the Construct
menu. Constructions remain true regardless of how the original object(s) are
See also Construction
Commands to program constructions within the Command Window.
Both a straight line (segment, ray, or line) and a point must be drawn
and selected to construct a parallel line.
Both a straight line (segment, ray, or line) and a point must be drawn
and selected to construct a perpendicular line.
Draw and select two objects to construct their intersection (e.g.,
circle and line).
The midpoints of all selected segments, and all selected
sides of figures or polygons will be constructed.
Both a circle and a point (on or off the circle) must be drawn and
selected to construct tangents.
Draw and select one angle to construct the angle bisector.
Draw and select two vectors to add them.
- Make sure the objects involved in the construction are the only objects
selected. See also selecting objects.
- Constructions can be performed on polygons; you may need to draw a superimposed
segment or angle first (the polygon is treated as one whole object, not as
separate parts). See also drawing objects.
Reflect (flip), Rotate (turn), Translate (slide), and Scale (stretch/shrink)
a drawn geometric object to a new location in the plane. Options for using
the Toolbar or Transform menu are explained below.
Note: The Toolbar options (, , , )
are best for dynamic transformations determined by clicking and dragging. The "___
By" Transform menu options are best for a fixed transformation within
the Coordinate environment.
See also Transformation Commands to perform
transformations within the Command Window.
- Select a drawn object and the line of reflection then choose Reflect
- Deselect all objects then choose Reflect ().
Click and drag from a drawn object for a dynamic reflection line. OR
- Select a drawn object then choose Reflect By. Type the coordinates
of a point (separated by a comma) on the desired reflection line through
the origin (this line cannot be changed once determined).
- Select a drawn object and an angle by which to rotate then choose
The angle determines the degree of the rotation in a counterclockwise
direction about its vertex. OR
- Deselect all objects then choose Rotate ().
Click and drag from a drawn object for a dynamic angle of rotation.
The center of rotation may be inside the object or defined by a vertex
(depending on where you click and drag from). OR
- Select a drawn object then choose Rotate By. Type the desired degree
of the angle of rotation to rotate the object counterclockwise about
the origin (this angle cannot be changed once determined).
- Select a drawn object and a segment then choose Translate ().
The direction and magnitude of the translation is determined by the
directed distance from the first toward the second point of the segment. OR
- Deselect all objects then choose Translate ().
Click and drag from a drawn object for a dynamic translation vector. OR
- Select a drawn object then choose Translate By. Type the desired
x- and y- components of the translation (this is fixed and cannot be
changed once determined).
- Select a drawn object and a segment then choose Scale ().
The direction and magnitude of the scale transformation is determined
by the directed distance from the first toward the second point of
the segment. OR
- Deselect all objects then choose Scale ().
Click and drag from a drawn object for a dynamic scale transformation
determined by a directed segment. OR
- Select a drawn object then choose Scale By. Type the desired x- and
y- components of the scale vector (this is fixed and cannot be changed
Use the Options and Edit menus to control the Settings. In general:
A Style Window will appear after either of these options is selected (see illustration
- use the Options menu to change the geometry environment settings for all
created objects at once or before objects are created (e.g., choose
Options | Default Settings, and the settings will apply to all subsequently
- use the Edit menu to modify stylistic aspects of selected objects after objects
are created (e.g., select Edit | Change Style of Selected and the
settings will apply to all currently selected objects).
See also Default Styles and Settings, Labels, Hide/Show
or Delete Objects, and Undo.
Access the Style Window to adjust the following
settings (Options | Default Settings OR Edit | Change
Style of Selected):
- Label objects (default on) by capital alphabetical labels in the
order they are created. See also Options | Hide
Labels (hides all at once), and Edit | Label
Change (replace default label)
- Show Coordinates (default off) labels points in Coordinate geometry
with ordered pairs. See also Options | Hide
- Filled objects (default off) will have their interior shaded according
to the "Select Fill Color" palette (default gray).
- Visible (default on) is only accessible within the Default Style
window (Options | Default Settings).
- The Font Size (default 12) of labeled objects can be increased or
- Thickness (default thin) of edges can be made thicker and Edge Color
(default black) can be changed by using the “Select Color” palette.
Default Styles and Settings
The main difference between Synthetic and Coordinate Geometry environments
is the Grid Style (see Options | Grid
Style). The Grid and Axes are off (not shown) for Synthetic and on (visible)
for Coordinate. In a Coordinate Geometry Environment the following
settings are applicable:
- Options | Snap to Grid (default
on) restricts the drawing of points to grid marks. When not checked plot
points with non-integer coordinates.
- Options | Hide Coordinates
(default off) will hide (or show) all coordinates at once. Use Edit | Change
Style of Selected to be more selective about which coordinates to show/hide.
- Options | Grid Style (default
on) allows one to modify the grid points, thickness, style, and color of
Help Tip: Coordinate Labels are ordered pairs attached to points
plotted in the coordinate plane and are a stylistic aspect of the geometry
environment. To compute with matrix representations of ordered pairs select
the desired object(s) choose Measurements | Coordinates.
- Options | Window Scale (default
20: [-10, 10]) takes a positive numerical value to set the viewing range
of the screen for both x- and y-axes (the screen will always be symmetrical
about the origin).
- Labels of drawn objects are shown by default. For
a selected object, choose Options | Hide Labels or Edit | Label
Change. For Label Change, the current name is in the left-hand column, the
new name is typed into the right-hand column. Close the window to change
See also Style Window (Edit | Change
Style of Selected OR Options | Default Settings).
- Hide/Show or Delete a selected object using
the appropriate Edit menu option (Edit | Hide Selected, Show Hidden,
Note: Show Hidden will make all previously hidden objects
visible. Delete Selected is permanent and cannot be reversed.
- Edit | Undo ()
reverses the most recently performed action(s).
Note: Deleted objects cannot be shown again. To temporarily hide/show
objects use Edit | Hide Selected.
Programming and Animation
Execute a sequence of commands to draw, construct, transform, and otherwise
manipulate objects in the plane.
See also Available Commands for
There are several avenues to pursue programming within Interactive Geometry.
Some are listed below:
- Use the Design by Robot Custom App to test the use of simple commands to
move the robot around the screen (e.g., fd 10 rt
90 to move forward 10 units and turn 90 degrees).
- Create a drawing or construction within Interactive Geometry. Choose File | Save
and use the .txt extension. Open this saved file within a Text Editor program
on your computer. Read through the programming commands that were used to
create the drawing you made. Also open a saved text file within Interactive
- Type into the Command Window (press Enter to execute a command).
To view the command window Choose Options | Command
Window, or move your cursor to the bottom of the screen and drag up from
the small circle.
- Type the program command
(followed by a space and the name of your program) into the Command Window
to work within the Program Editor. Close this window then call the program
by typing its name. This is especially useful for longer programs or animations.
(type program into programming window, then close window)
See also programming Basics.
- See the Available Commands for Geometry.
- Do not use reserved words such as point or circle to
name objects or programs. For example, a good command would be let
pointA=point [0,0] (the name of the point is "pointA").
Other reserved words include but are not limited to:
draw, polygon, point, segment, ray, line, halfplane,
circle, angle, parallel, perpendicular, intersection, midpoint, clear,
let, cs, info, show, reflect, rotate, translate, scale, visible
- A space " " should follow all reserved word commands.
- Square brackets are used to enclose commands and ordered pairs (e.g., let
segmentAB=segment [[0,0][5,3]], let M=[midpoint segmentAB]).
- let and draw (or visible)
are basic commands to define and show objects.
- Clear the screen (cs)
or the screen and command window contents (clear).
- The information or coordinates of an object can be shown on the screen
within the command window (show).
- Commands for defining and drawing common objects
include: angle, circle, halfplane, line, point, polygon, ray, segment, vector.
See also Drawing using the menubar/toolbar.
- Construction commands include: bisect, intersection, midpoint, parallel, perpendicular, tangents.
See also and Constructions using
- Transformation commands include: reflect, rotate, scale, translate.
See also Transformations using
- Additional commands include: input "Prompt" variable, path
Note: Common functions that can be used with the [function
expression] syntax include abs, cos, invcos, invsin, invtan, sin, sqrt, tan.
An animation is a sequence of programming commands that often involves drawing,
constructing, and transforming objects in the plane. For ease in executing
several commands at once, use the program command.
Consider the following annotated example of a simple animation using
scale transformations. Note that with this option, few lines of code are typed
into the Command Window. Most coding is done in a separate Program Window which
allows for greater flexibility and editing of a sequence of commands.
||• A new window with title growShrink will appear.
let wheel = [circle [[0,0][1,0]]]
Style wheel visible on fillcolor 255 0 0 filled on
repeat 10 [draw [let wheel = [scale wheel 1.3]] pause 100]
repeat 10 [draw [let wheel = [scale wheel .77]] pause 100]
|• Enter the program commands into the new window. Close the window
||• To run the program, type just the name into the Command Window.
||• To edit the program, type the to command
followed by the name of the program. Alternatively, type the program command
followed by the name of the program. The Program Window will be shown.