The shape files created by GeoMedia will only have the following files created: .dbf, .shp, and .shx, as shown in the screen shot below. GeoMedia will also create a file with the extension .csf that contains the coordinate system of the exported shape file. However, this is a proprietary file and can only be read using Intergraph software.
When these GeoMedia created shape files are read in ArcMap with the Layer | Add Data command as shown below, ArcGis will not be able to determine the correct coordinate system and the software will pop up a warning message:
The shape files can be displayed in ArcMap but the coordinates are plain XY coordinates; the units and projection are unknown as highlighted in red below. The shape layers cannot be reprojected to another projection system.
In order to resolve this problem, ArcGis users will have to create the .prj file by copying over some existing .prj file from perhaps the ArcGis product folder or through some other means. This task can get very tedious if there are a large number of shape files.
If the shape files have associated .prj files, then ArcMap can read the shape files including the coordinate system defined in the .prj file successfully, as shown in the figure below. Note the projection information highlighted in red.