Let ABCD be a tetrahedron, G, G' and G" the centers of gravity of faces ABC, ACD and ADB, I and J the midpoints of edges [BC] and [CD].
1) Show that lines (IJ) and (GG' ) are parallel.
2) Prove that the points G, G' and G" are not aligned.
3) Show that the planes (GG 'G ") and (BCD) are parallel.
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