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Why parallelogram is always formed?

Author:
Terry Tam
Topic:
Parallelogram
ABCD is a quadrilateral, and E, F, G, H are the midpoints of 4 sides of ABCD. Prove that EFGH is a parallelogram. How about ABCD is concave? How about ABCD is crossed? [Varignon's theorem] (Hint: Consider diagonals)

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