I want to fix a broken lampshade, but no glue seems to work on hard plastic. Is there any way to salvage it?

Hard plastic has always been a real challenge for the glue manufacturers but they have finally solved the problem by using two glues to get the job done. Rigid plastic adhesive consists of two parts: a primer and the glue itself. The primer is a very thin liquid that has the ability to stick to the smooth surface of plastic. First prepare the surfaces to be glued. Because rigid plastic adhesive will not fill gaps, the two surfaces have to fit perfectly together. The strength of rigid plastic adhesive is proportional to the surface area being glued, so narrow edges won't hold as well as overlapped pieces of plastic. Apply the primer to both surfaces to be glued together. Be prepared to work quickly, as the primer dries within a minute. Next apply the glue to only one surface, and put the pieces together. There is no need of clamping; the beauty of rigid plastic adhesive is that you only need to hold it together for 20 seconds, then it will hold itself. Don't test it yet, as it takes about12 hours to cure properly. Then your lamp should be as good as new.