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Midpoints on a tetahedron

Source: Romanian District Olympiad 2004, Grade X, Problem 3

October 7, 2018
geometry3D geometrytetrahedrongeometric transformationrotation

Problem Statement

On the tetrahedron ABCD ABCD make the notation M,N,P,Q, M,N,P,Q, for the midpoints of AB,CD,AC, AB,CD,AC, respectively, BD. BD. Additionally, we know that MN MN is the common perpendicular of AB,CD, AB,CD, and PQ PQ is the common perpendicular of AC,BD. AC,BD. Show that AB=CD,BC=DA,AC=BD. AB=CD, BC=DA, AC=BD.
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