The polyhedron PABCDQ has the form shown in the figure. It is known that ABCD is parallelogram, the planes of the triangles of the PAC and PBD mutually perpendicular, and also mutually perpendicular are the planes of triangles QAC and QBC. Each face of this polyhedron is painted black or white so that the faces that have a common edge are painted in different colors. Prove that the sum of the squares of the areas of the black faces is equal to the sum of the squares of the areas of the white faces.
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