Geometry Software
last updated 10/17/12
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GeoGebra
This is by far my favorite DGE (dynamic geometry environment). This software does a ton of stuff and does it extremely well. You can make constructions with points, vectors, segments, lines, polygons, conic sections, and even functions. By including functions, it ties together the link between algebra and geometry quite nicely. Along with using it in geometry, I've even used it in calculus for applications like area under the curve. I'd recommend it to anyone looking for a free version of Geometer's Sketchpad. The user interface is fairly intuitive, but also allows for advanced user input by use of a text input bar along the bottom. Be aware that using the text bar along the bottom assumes a basic knowledge of programming skills.  My only wish is that it would support non-Euclidean geomtries.  It should also be noted that they are currently working on implementing a robust 3d geometry environment.
Geogebra screenshot

NonEuclid
This is a DGE for exploring NonEuclidean geometry.  It models both the disc and the upper half-plane model.  It is not nearly as robust as the other software listed, but is one of the best ways get a grasp on hyperbolic geometry. It allows for basic constructions but is limited on the types of measurements and calculations you can do with those constructions. This limitation is mainly due to the lack of an in-program calculator. It has a nice help menu that links you to many activities that students can complete to gain understanding.
NonEuclid Screenshot

CaRMetal

This is a DGE for Euclidean geometry, hyperbolic, and some basic 3D geometry.  The interface isn't as intuitive as the others but I appreciate the various geometries in one package.  My main complaint with the interface is how to do calculations.  I believe it can do calculations, but I've found it cumbersome (or maybe I just haven't used it enough).  On a positive note, it includes some very easy to use 'property checkers'.  For example, you can click two lines, and it can tell you if they are parallel.  It is a great way to test theories before you start trying to prove it.  Also, (and perhaps my favorite feature), I love the fact that it has a Monkey button!  That alone makes this awesome.  The Monkey button "shakes" the drawing to make sure the figures are constructed properly.  In other words, I can 'construct' shapes that look correct, until the Monkey shakes the screen.  With a proper construction, the shape should remain intact.  It is worth noting that many of the resources for this software are in French.
CaRMetal screen