DGPad software allows dynamic geometry constructions. Particular care has been taken in GUI design and human interface, so this application can be easily used with students in classrooms with tablets.
You can perform all constructions via contextual tools which only appear when you tap on a geometric object : then you just have to hold your finger on the tool and drag until you reach the target object.
While dragging your finger after you selected a tool, it's possible to create objects on the fly. Existing objects will always react (graphical highlight of target objects) to tell the user that he's about to create a point on object, or at an intersection. More generally, graphical feedbacks will always be present during construction process. This will let the user, especially if he's a young student, to understand what he is about to do.
You can also make your own tools (macro-constructions) to design more complex figures.
For segments, lines and polygons, you can also use a track tool (second icon in bottom control panel) to dynamically construct these objects, just by sliding your finger on screen.
You can hide objects and change their display properties by using a tactile property panel (sixth icon of bottom control panel)
DGPad is also a free webApp, but this application allows you much more features, like working without network, or opening DGPad files (even if these files are stored locally in your iPad) using the "open with..." functionality of other softwares Download center, DropBox, GoogleDrive, SkyDrive, etc...