Question 1009866
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Look into the lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/word/geometry/Midpoints-of-a-quadrilateral-are-vertices-of-the-parallelogram.lesson>Midpoints of a quadrilateral are vertices of the parallelogram</A>&nbsp; in this site.


The Theorem is proved there:

In an arbitrary convex quadrilateral the midpoints of its sides are vertices of the parallelogram.


If you add the facts that 


&nbsp;&nbsp;&nbsp;&nbsp;in a square the diagonals are congruent,


and


&nbsp;&nbsp;&nbsp;&nbsp;in a square diagonals are perpendicular,


then you will get the proof that you requested.


Please let me know in the "Thank you" section, if you need more explanations.

Do not forget to place the number of the problem (# 1009866) in order I could identify it.