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Reverse engineering allows the geometric reconstruction of simple mechanical parts. However, the resulting models suffer from inaccuracies caused by errors in measurement and reconstruction so such models do not have the exact congruence, symmetries and other regularities the original designer intended. We wish to impose such regularities in a beautification process. The paper discusses the particular problem of detecting approximate congruence between parts (e.g. a pair of handles) of a reconstructed B-rep model, so that a subsequent step can enforce them exactly. A practical detection algorithm is given for models defined using planes, spheres, cylinders, cones and tori. Analysis of the algorithm and experimental results show that expected congruence are detected reasonably quickly.