This afternoon I discovered Google SketchUp and tested its ability to do geometric constructions. The most difficult problem I had was doing line and angle bisections but these tasks can be accomplished by using the protractor tool to draw guide lines at fixed angles to find points of intersection similar to those found with a compass. The figure did not come out as precise as I would have liked but tinkering with the settings would probably help.
This construction of the pentagon is my first effort using SketchUp. It might help if there was a compass tool for marking off fixed distances along a line and drawing arcs a fixed distance from a point.