This question is about fitting two jigsaw pieces back into one square. Panel I is one piece of square PQRS, and we must find the second piece from the four shapes in Panel II that closes the square exactly.
(i): this shape has a comb-like top that does not match the step pattern along the cut edge of Panel I, so placing it next to Panel I leaves uneven gaps.
(ii): this is close in outline to (i) but with the teeth shifted slightly, and it still does not line up with the notches of Panel I.
(iii): this staircase shaped piece has each step sitting flush against a notch in Panel I, so the two pieces together retrace the straight sides of the original square.
(iv): this looks similar to (iii) but the steps are shifted by one position, so a small gap or overlap appears where the pieces should meet.
Since only shape (iii) interlocks perfectly with Panel I along every step of the cut, it is the missing part of square PQRS.
Let's summarize:
The two pieces of a cut square must interlock at every notch with no gap or overlap.
Shapes (i) and (ii) belong to a different outline family and do not match the cut at all.
Shape (iv) matches the family but is offset by one step, while shape (iii) lines up exactly.
