Reflecting Squarely
An excellent solution from Andrei of School 205 Bucharest. I like this very much because of the effective and systematic approach he took to investigating the problem.
Here is Andrei's solution:
I worked systematically. I took the big (yellow) piece and I placed the rectangle in all the possible locations around it (both vertically and horizontally). Then I looked if the figure admitted a symmetry line (vertical, horizontal, or at a 45$^{\circ}$ angle) if I added a small square (blue). Here is all my work and the solutions I found, with the corresponding symmetry line:
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