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I am confused as to how to proceed with this proof. Any help in guiding me through it step by step would be greatly appreciated.

Prove that the quadrilateral EFGH whose vertices are the midpoints of the sides of an arbitrary quadrilateral ABCD is a parallelogram.

I answered this question for Nick on 1/18/13; using his figure, here is my answer:

"From your figure, consider the points A, D and C and the distance between points A and C = |AC|. Using the relationships for similar triangles, the distance between the mid-points S and B is |SB| = (1/2)|AC| and SB is paralell to AC. SImilarly, the line segment |PQ| = |SB| and these 2 segments are paralell.

Using the same approach, it can be shown that the segments SP and RQ are also equal and paralell. The 4 segments together thus form a paralellogram."

I wish I could copy his figure but the system makes it very hard. If you look on the site for 1/18/13 under my name you should find it. Good luck. Follow-up with me if you have trouble.

Randy

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