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Figure A pictorial representation of the relations to be analysed in a GIS for moving a factory from an old to a new site  Note that the production lines of the new facility may not be suitable for hosting certain engines

- There is at least one roto translation in which y coincides with a proper part of x The region x has a proper part congruent to y
- None of the above The region x and y cannot be perfectly overlapped We would like to stress here three main aspects of these relations The relations can be established between two spatial regions in any position of space There is no specific need for the regions to be close  or to be in any particular topolog ical relation provided that the relation is compatible so these congruence relations are purely morphological The equality of two regions implies congruence The relation of proper part excludes morphological relations other than  congruent to a part"  This is not the case for the morphological side A region can be congruent to a part of another region  even if they are disjoint  and the same can happen to congruence  as already stated in point Even if two regions are of the same size  there may be the case that the regions are not congruent This holds also for partial congruence being possible that a region is smaller than another one but they cannot be overlapped The practical relevance of the algebra can be proved by exhibiting many other examples especially coming from GIS In this paper we deal with the problem of reasoning about congruence in two dimensional space domain The kind of congruence we assume is the weakest one  roto translability  Three dimensional congruence is not of the same type  The natural" notion of three dimensional congruence is isometry which is much more general than roto translability For example left and right hands are congruent under the simplified assumption that they have the same shape and size but they cannot be roto translated each into the other one   We concentrate here in two dimensional reasoning which may be