Let A, B, C, and D be four points in R3 such that no three of them lie on a line. Then ABCD is a quadrilateral, though not necessarily one that lies in a plane. Denote the midpoints of the four sides of ABCD by M1, M2, M3, and M4. Use vectors to show that, amazingly, M1M2M3M4 is always a parallelogram.
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