Problem

Source: Romania TST 5 2009, Problem 1

Tags: algebra, function, domain, geometry, geometric transformation, rotation, geometry proposed



Given two (identical) polygonal domains in the Euclidean plane, it is not possible in general to superpose the two using only translations and rotations. Prove that this can however be achieved by splitting one of the domains into a finite number of polygonal subdomains which then fit together, via translations and rotations in the plane, to recover the other domain.