Stage: 4 Challenge Level: 
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.
Created with GeoGebra
Generalising. Dynamic geometry. Fibonacci sequence. Interactivities. Mathematical reasoning & proof. Making and proving conjectures. Enlargements. Similarity. Parallelograms. Quadrilaterals.
Published June 1998.
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