Select the figure from the given four alternatives which fits exactly into…

Concept

In a “complete the square” (figure-completion) puzzle, the given main piece and the correct option are two complementary parts of one whole square that meet along a single shared cut. So the inner cut-edge of the correct piece must be the exact negative of the main piece’s open edge: every projection on one side meets a matching recess on the other, and a sloping (diagonal) edge on one part must be answered by a collinear diagonal on the other, so the two diagonals merge into one straight line in the assembled square. The piece may need to be mentally rotated into place; what must match is the cut-edge profile, not the orientation as drawn.

Applying it to this figure

1. Read the open (cut) edge of the main piece, Figure-X. Its top edge and right edge are straight and complete; the cut is carved out of its lower-left, where the boundary forms a small rectangular notch (an inward step) and then a straight diagonal that runs down to the bottom-right corner.

2. The piece that closes the square must therefore carry the negative of that cut: a single straight diagonal that meets a single rectangular step, so that the step plugs the notch and the diagonal lies flush against Figure-X’s diagonal.

3. Test each option by its cut-edge profile, ignoring how it happens to be turned: the required piece shows exactly one diagonal feeding into one rectangular step — no extra stair-treads and no second diagonal.

4. The piece whose cut edge is a single diagonal running into one rectangular step has this exact mating profile; rotated into Figure-X its step fills the notch and its diagonal becomes collinear with Figure-X’s diagonal, giving the completed square shown in the figure above.

Cross-check (why the others do not mate)

• The piece built as a two-step staircase with a long diagonal along one edge offers two stair-treads where the cut needs a single notch; its profile cannot seat against Figure-X’s notch-and-diagonal edge no matter how it is turned.

• The piece with a peaked diagonal, a square tab jutting from its side and a wide flat foot has no diagonal-into-single-step edge at all, so there is no profile that meets Figure-X’s cut.

• The piece that is itself a filled corner carrying an internal staircase and diagonal repeats the kind of solid region Figure-X already contains; placed against it the solids overlap and leave gaps instead of closing the square.

• Only the single-diagonal-into-one-step profile is the true negative of Figure-X’s cut, which is why it alone rebuilds the complete square.