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 nonEuclidean geomtries. It should also be noted
that they are currently working on implementing a robust 3d geometry
environment. 
NonEuclid 
This
is a DGE for exploring
NonEuclidean geometry. It models both the disc and the upper
halfplane 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 inprogram calculator. It
has a nice help menu that links you to many activities that students
can
complete to gain understanding. 
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. 