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property of tatrahedron with opposite edges equal

Source: Polish MO Finals 1954 p5

August 29, 2024
geometry3D geometrytetrahedron

Problem Statement

Prove that if in a tetrahedron ABCD ABCD opposite edges are equal, i.e. AB=CD AB = CD , AC=BD AC = BD , AD=BC AD = BC , then the lines passing through the midpoints of opposite edges are mutually perpendicular and are the axes of symmetry of the tetrahedron.
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