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ASU 358 All Soviet Union MO 1983 // planes, projections of tetrahedron

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July 28, 2019
3D geometrygeometrycombinatorial geometryplanesparallelprojectiontetrahedron

Problem Statement

The points A1,B1,C1,D1A_1,B_1,C_1,D_1 and A2,B2,C2,D2A_2,B_2,C_2,D_2 are orthogonal projections of the ABCDABCD tetrahedron vertices on two planes. Prove that it is possible to move one of the planes to provide the parallelness of lines (A1A2),(B1B2),(C1C2)(A_1A_2), (B_1B_2), (C_1C_2) and (D1D2)(D_1D_2) .
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