You can draw up to 4 straight lines in order to create 10 equal squares in the following figure:
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I need 12 lines - 8 to find the centers of the large squares (thanks Aragaer for noticing that we get the center "for free"), then 4 to create the 10 equal squares. You could argue that the 10 dashed lines are not drawn as part of the "creating squares". In fact, you could use a ruler to draw just the little orange "helper marks" in order to do the construction.
It does assume that the two initial shapes are squares.