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## 'Quad in Quad' printed from http://nrich.maths.org/

ABCD is a convex quadrilateral. The points P, Q, R and S are
the midpoints of the edges of ABCD. You can change the shape of the
quadrilateral ABCD.

What do you notice about the quadrilateral PQRS as ABCD
changes?

Is the area of PQRS always the same fraction of the area of ABCD
and, if so, what is this fraction?

Try to prove your conjectures.

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