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 congruences, symmetries and other regularities the original designer intended. We wish to impose such regularities in a beautification process. This paper discusses the particular problem of detecting approximate congruences 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 congruences are detected reasonably quickly.