Stage: 4 Challenge Level: 
ABCD is a non-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 and its area as ABCD changes?
If you say that what you have noticed is always true, then you are making a conjecture. Can you prove your conjecture?
Created with GeoGebra
Mathematical reasoning & proof. Dynamic geometry. Summation of series. epsilons. Fibonacci sequence. Making and proving conjectures. Parallelograms. Interactivities. Generalising. Stage 5 - Reviewed 2012.
Published July 1998.
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