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?