Geometer's Sketchpad

(Please bear with me as I edit this and add hardlinks.) This is an excellent program, especially for high school students who are starting to learn complicated geometric properties. You can construct a plethora¹ of different geometric figures:

• A point. (Simple, huh?)
• A circle. (Defined by a point and a radius) or an arc (defined by three points)
• A line, ray, or line segment. (Defined by two points)

And then, you can construct other figures onto one you've already put down. Ie, you create a circle, place a point on top of it, then create a line through this point and the center of a circle.
Using this program, I've successfully constructed conic sections (parabolas, ellipses, hyperbolas) and also illustrated problems for my classes. (For those of us who have visual minds, it is very helpful to do this.)
Other things you can do:

• Create a line through a point that is perpendicular or parallel to another line.
• Create a point at the intersection of two figures, or a point at the midpoint of a line segment.
• Create a bisector of an angle
• A circle defined by a center and the length of it's radius (ie. a measured distance, or a number)
• An area defined by a polygon or another figure.
• A locus ( more on that later)

You can also do transformations on a figure:

• Translate it by a given vector (rectangular or polar coordinates) or by one defined by another figure in your sketch, which could be variable.
• Rotate it by some angle around a marked point
• Dilate it by some scalar with respect to a point
• Reflect it across a line

You can do all sorts of measurements. You can measure:

• Distance between two points
• Length of a segment or an arc
• Slope of a figure
• Radius of a circle or arc
• Circumfrence
• Area
• Perimeter
• Angle (given a center and two points, or an arc)
• Ratio of two measurements
• Coordinates (when a coordinate system has been defined

On top of all that you can enter an equation where the measurements are the variables, and then use that to define some part of your figure.
A locus is really neat. You start with a point that is defined to be on a path (ie. on a circle or a line or somesuch) and another point that is somehow affected by the position of the first point. You can then construct a locus, which is the set of all the positions that point 2 encounters as point 1 moves along its path. It then stays there while you manipulate the figure. You can use this to construct say, a parabola, and then move the directrix and the focus around to see how the parabola changes.
You can also animate things, by telling the program to animate one point along its path and you can then see the rest of the figure bend and twist or whatever as this happens.
You can also add in labels, colors (pretty colors!) and text.
The Geometer's sketchpad also comes with a very nice and easy-to-use macro utility, it allows you to recreate a construction you made multiple times and in multiple projects. Nice!

The Geometer's sketchpad was created by Nickolas Jakiw and is © Key Curriculum Press. It works on Win32, but older versions work on Windows 3.1 as well.

¹ I'm always looking for a place to use that word.