We have rectangle sheet, and a small rectangle piece cut inside it at RANDOM place. How to make make that sheet into exact same 2 halves?
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If you do a cut through the center of a rectangle, no matter at what angle, this rectangle will be divided in half.
Thus, if we make a cut through the center of the cutout rectangle, each side of the cut will have 50% of the cutout area. And if we — at the same time — cut through the center of the large rectangle, this should do it. Both sides of the cut have half the area of the large rectangle, minus half the size of the cutout.
Of course, that is if by “exact same 2 halves” you mean same area, but not necessarily same shape. The latter will generally not be possible.