Set a plane on an object

Hello guys!

It is really difficult for me to write in english but I'm going to try my best. 

The problem is that I want to put a plane such as xy-plane or xz-plane on a 3d object which is located across the room. The plane has to lie parallel to the surface of the object. So I tried a few thing until it worked somehow; I'm going to upload a picture of it. By the way I'm totally a beginner. 

I placed a few points on the 3d object and vertical above them the same amount of points again. After that I defined planes to the points above and replaced them to the points below with "plane origin". But to do that I had to change the plane of the 3d object in rhino so that the planes with the points are placed parallel to the surface of the 3d object. However it just seems too complicated, is there another way which is a lot easier? Any tips and tricks maybe? I have to do that because I need to define the tool path of a robot. 

Thanks a lot for any feedback
Tülin