My data frame projection is WGS 84 (taken from the several ESRI basemaps loaded in the data frame). I brought in some GPS points which were taken in NAD27. They were projected on the fly to match the data frame projection. I need to create a polygon based on these GPS points. I'll eventually need the polygon information to be in NAD27. My question is: because I'm creating a shapefile based on the GPS points in WGS84, do I need to set the new shapefile projection to WGS84? Or can I set the projection to NAD27, then, as I create the polygons, they will be shown correctly in the data frame, and still truly be NAD27?