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criterion for perpendicularity of edges AB and CD of tetrahedron ABCD

Source: Polish second round 1998 p6

January 19, 2020
perpendiculartetrahedron3D geometrygeometry

Problem Statement

Prove that the edges ABAB and CDCD of a tetrahedron ABCDABCD are perpendicular if and only if there exists a parallelogram CDPQCDPQ such that PA=PB=PDPA = PB = PD and QA=QB=QCQA = QB = QC.
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