Interactive plane geometry software were made popular first by Geometer's Sketchpad at least back to 1994. It is a wonderful tool made possible by technology. Such program allows one to construct plane geometry drawings dynamically, much in the way of Greek's “Ruler and Compass”. For example, draw a triangle with lines bisecting the 3 angles. They intersect in a point called the incenter of the triangle. (which is also the center of the largest possible circle inside.) Now, you can drag the corners of your triangle to change its shape, and all your drawings change accordingly. Because of such dynamic power, a few theories on plane geometry have been found because of such software.
In the 1990s, there's only Geometer's Sketchpad and Cabri Geometry. In late 1990 came Cinderella (software), written in Java. But since about post 2000, there's a explosion of interactive geometry software. As of 2007, there are more than ten of them (counting only quality ones), many of them are free. They are all similar. They are all of high quality. Almost all of them can be saved as Java appletes so that it can be placed on the web for students to use without needing extra software. Their features differ slightly. Several of them are FreeSoftware. The following is a short commentary of the ones i've actually used (except otherwise stated).
GeoGebra is a interactive geometry software. Written by Markus Hohenwarter, started in 2001. Of all interactive geometry software i've used since 1996, i recommend GeoGebra if you don't have specific requirement. Home page: http://www.geogebra.org/ Java
For some sample files of GeoGebra, see deltoid curve, cross curve, nephroid curve .
ZuL is written in Java by von R Grothmann. This program is excellent. It is very well written, in Java and available for Mac or Windows or Linux, and it is free with source code too. Its home page is at http://www.rene-grothmann.de/car.html Java
The Geometer's Sketchpad, created by Nicholas Jackiw. This is the one that started dynamic geometry software in the early 1990s, and is still excellent. OSXMacWin
Over 100 sketchpad files are available at Visual Dictionary of Special Plane Curves.
Cabri II Plus, developed in France. Cabri is one of the early interactive geometry software in the mid 1990s. Cabri has a hardware TI calculator version. A particular feature that is first done by Cabri is that it has conics sections as a primitive. That is, you can have 5 points that defines a conic section, that is any of parabola, ellipse, hyperbola. Dragging any of the points will change the conics section. Any other figures build on the conic section will of course change accordingly. This makes Cabri a excellent choice for doing projective geometry.
Cabri demo can be downloaded at Cabri home page http://www.cabri.com/. MacWinJava
Geometry Expressions There is a new interactive dynamic plane geometry software, called Geometry Expressions. However, this one is different from all the others because it does symbolic geometry. I haven't tried it yet, but hope to review the Mac version soon. Commercial. http://www.geometryexpressions.com/index.php win