Geometry software

One of my children is taking Geometry this year, which is turning out to be a lot of fun. We have a nice compass and a good ruler, but even with these good tools construction can be a little tedious, especially for complicated problems. Geometry software is a good compromise because it can take some tedious compound operations and do them in one click; these are things you pick up early on (construct a perpendicular to a line, perpendicular bisector to a segment, parallel lines, reflection about a line, etc.) and do them later as a single step.

UPDATED to add:This article from Science Daily talks about how using Geometry software helps students play with construction concepts more readily than with paper and tools. It also suggests that the software is helpful to teachers, and that it's important to students to learn to use both the software and the physical tools.

I've heard that Geometer's Sketchpad is well regarded by math teachers. I love Key Curriculum Press textbooks; their materials and problem sets are compelling and fun. However, this piece of software doesn't work for our family for two reasons:

1. It won't run on Linux (only Mac OSX or MS Windows), and
2. it's not free software.

Luckily, there are good alternatives!

• C.a.R. and C.a.R.metal. C.a.R. stands for "Compass and Ruler"; it's a program which lets you perform all kinds of constructions using those tools. The array of available options is initially a bit daunting; it's very helpful to go through the tutorials first. You can set up a problem and have a second person solve it; the software will report if you get the right answer. The software will also allow graph a function for you; it's more intuitive in C.a.R. than in C.a.R.metal, but it's possible in both.
• Another interesting piece of software is Geometria. It's designed specifically around the presentation and solution of construction problems. To use it you must create a problem to be solved, then convey the problem to a student. As the student works on the problem, each step is recorded in a history log on the left side; this is useful for documenting a proof based on the construction steps. This program is not as free-form as the others, so I've not played with it much; still, I can see this being very useful for a teacher, who can create one problem and hand it out to the class. I also expect it won't be long before there's a collection of problems you can download for your class. You can try a demo online; I'd keep another tab with the documentation open while you're using it.
• Finally there's GeoGebra, a slick tool which does a good job of both geometry and algebra. It can be used on the web here if you want to try it out. It's got the best support for plotting functions and equations of the three; unfortunately, it's not entirely free software (the software/program is free, released under the GNU Public License, but the on-screen messages, which are translated into different languages, are not).

I like Key Curriculum Press; if you do too, want to support them financially, and have MS Windows or Mac OSX, go ahead and get a copy of Geometer's Sketchpad. Even so, you might want to play with the software packages above. They're all well written, and it's fun to play with a compass and ruler and see what you can construct.