Matching up similar UV islands perfectly

I have a mesh consisting of several identical shapes. some of these identical shapes I want to match up perfectly on UV image. When I unwrap them they come out similar but not identical, and i can grab/rotate them and get them pretty close but the don’t exactly match up. Is there an easy way to do this other than meticulously placing every vert on the UV map?

You can select multiple points and W/weld them together or use press the magnet icon to activate snapping (select to vertex). Similar tools are available in the uv editor as are in the 3d view so there are many ways to line things up precisely.

Thanks, i’m doing the weld now. a little tedious but not too bad.