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-tha

Question Number 157087 by henderson last updated on 19/Oct/21

$$ \\ $$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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