# Possibilities

• Modeling of geometric constructions: performing construction with the imitation of ruler and compass, exploration of the resulting configuration, carrying out measurements.
• Advantages of interactive geometry: instant change of all dependent parts of a construction and recalculation of measurements when user changes some basic parameters (drags a point).
• Creating live visual illustrations, interactive and dynamic learning materials, reference books and “expert systems”, using comments, buttons, hints and hyperlinks.
• Organization of computer experiments and explorations, forming hypotheses and checking their plausibility.

# In detail…

DG allows to:

### Carry out constructions, analogous to classic ruler-and-compass constructions:

• Draw points.
• Draw segments, rays and lines.
• Draw circles given their center and point on a circumference.
• Construct circles with given radius.
• Construct distances and angles equal to given.
• Draw parallel and perpendicular lines, bisectors.
• Construct points on figures.
• Find intersection points of figures.
• Find symmetric points and inverted points, draw segment midpoins.

### Measure drawing parameters (distances, angles, areas, coordinates, etc.).

Measurements also update instantly when basic parameters change. This feature provides wide possibilities for explorations, search of regularities and patterns, and formation of hypotheses. Measurements can be carried out in three ways:

• Direct measurement via measurement tools (creation of measurement marks near object being measured).
• Adding a text label that contains a dynamic expression in brackets. In this way any correct mathematical expression will be evaluated and its result will appear in a label text.
• With the aid of built-in geometric calculator, which as well allows to evaluate expressions.

### Automate the process of construction

by defining a new tool – creating a macro.

### Use elements of analytic geometry

coordinate system, equations of lines and circles, algebraic dependencies between parts of a construction, function plots, etc.

Specify figures and points analytically, i.e. given equations or functions for coordinates (5 types of line equation, 2 types of circle equation), especially analytic curves and function plots.

### Design and arrange a drawing:

edit visual properties of points and figures: names, color, draw width and mode, hide auxiliary elements.

### Construct locus of a point (geometric place of points)

trace the point as it moves, configure loci appearance, construct dynamic loci.

### Create interactive elements

buttons that allow user to show/hide objects, get hints, use multimedia and hyperlinks.

### Replay construction algorithm step-by-step.

Export drawings to graphic file formats (BMP, EMF, WMF) to create geometric illustrations, export the drawing into JavaSketchpad (© 2001 Key Curriculum Press) HTML format.