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Interactive Geometry

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 include:

  1. choose Draw | Segment then Construct | Midpoint;
  2. choose then ; or
  3. 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 option.

See also Draw Commands, and the Measure and Calculate features.

Figure or Polygon

Click once for each vertex, then double-click to end.

Point

Click once to place a new point; place a point on a drawn object once highlighted.

Segment

Click and drag from first endpoint to second, or select two points.

Ray

Click and drag from first endpoint to second, or select two points.

Line

Click and drag from one point on the line to another, or select two points.

Half Plane

Click and drag from one point on the line of the half plane to another, or select two points.

Circle

Click and drag from center of circle to a point on the circle.

Angle

Click three times to define a point, vertex, and another point; angle is determined counterclockwise from initial to final.

Vector

Click and drag from initial point to second point, or select two points.

 

Selecting Objects

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:

Choose Measurements | Calculation to perform a calculation using numerical values, or previously-calculated results or measurements. Within a Calculation window:

  1. Type the desired calculation (e.g., +, -, /, *); click on the drop-down list to insert an existing measurement or result.
  2. Choose a label for the calculation (or leave it blank) and click the Test button (this is what will display on the screen).
  3. Click OK to insert this labeled calculation into your drawing.

 

Constructions

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 dragged.

See also Construction Commands to program constructions within the Command Window.

Parallel

Both a straight line (segment, ray, or line) and a point must be drawn and selected to construct a parallel line.

Perpendicular

Both a straight line (segment, ray, or line) and a point must be drawn and selected to construct a perpendicular line.

Intersection

Draw and select two objects to construct their intersection (e.g., circle and line).

Midpoint

The midpoints of all selected segments, and all selected sides of figures or polygons will be constructed.

Tangents

Both a circle and a point (on or off the circle) must be drawn and selected to construct tangents.

Angle Bisector

Draw and select one angle to construct the angle bisector.

Add Vectors

Draw and select two vectors to add them.

Trouble-shooting Tips:

 

Transformations

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.

Reflect
  • Select a drawn object and the line of reflection then choose Reflect (). OR
  • 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).
Rotate
  • Select a drawn object and an angle by which to rotate then choose Rotate (). 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).
Translate
  • 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).
Scale
  • 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 once determined).

 

Settings

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 below).
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 Coordinates.
  • 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 decreased.
  • 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:

 

Programming and Animation

Execute a sequence of commands to draw, construct, transform, and otherwise manipulate objects in the plane.

See also Available Commands for Geometry.

Getting Started

There are several avenues to pursue programming within Interactive Geometry. Some are listed below:

See also programming Basics.

Basics

 

Animation

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.
program growShrink • A new window with title growShrink will appear.
cs
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]
end
• Enter the program commands into the new window. Close the window when finished.
growShrink • To run the program, type just the name into the Command Window.
to growShrink • 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.