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Yes, you can, and there are infinitely many ways of doing so.

1) Connect the midpoints

2) Notice the parallelogram shape

3) Double the length of one of the sides, and draw it parallel to that side

4) Match the ends of that line to the midpoints.

5) Voila! A quadrilateral with the 4 points as midpoints.

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Q: Can you draw a quadrilateral given only the midpoints of the sides and if so how?
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