The problem of finding approximate matches of pieces of shapes to parts of larger shapes is investigated. The shapes are represented by polygonal approximations. Initially, figures of merit are assigned to the matches between pairs of angles on the two shapes. Relaxation methods are then used to find acceptable combinations of these matches. This approach was tested on a data base consisting of digitized coastlines in various map projections. In nearly all cases, all matches except the correct one were eliminated by the relaxation processes.