MathDB

358

Part of 1983 All Soviet Union Mathematical Olympiad

Problems(1)

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

Source:

7/28/2019
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) .
3D geometrygeometrycombinatorial geometryplanesparallelprojectiontetrahedron