I think you can't use a straight line with the divide tool, it has to have at least 2 or 3 segments, I'm not sure. You can do them out of the territory, so the division is going to be a straight line.
I think I wasn't clear so you I think this picture can help you.
I have Inkscape on Spanish so I'm not sure if it is ok with "Path => Division" but I think you may understand.
Edited 8/21/2014 20:48:05