Select the alternative which represents three out of the five alternative…

In a figure-formation (assembling) puzzle, the accompanying key diagram shows the target outline actually being built from three specific pieces. The three correct answer-figures are exactly the three pieces used in that construction: each must be a plain, straight-sided polygon matching one of those pieces in shape. A figure that is not itself a simple triangle -- one whose own outline is concave, notched, or stepped -- cannot match a plain-triangle piece, so it cannot be one of the three correct figures here.

The key diagram shows the square split, using one full diagonal plus a second line from the midpoint of that diagonal to the opposite corner, into three triangular pieces; the accompanying image demonstrates that figures (1), (4) and (5) are exactly the pieces used in that construction. Among the five given figures, only (1), (4) and (5) are plain triangles bounded by three straight sides. Figures (2) and (3) are not triangles at all: figure (2) has a zig-zag outline with an inward, reflex point, and figure (3) has a stepped, L-shaped outline with a right-angle notch -- neither matches any piece of this three-piece construction.

The image above shows this construction: the square split along one full diagonal plus a line from the midpoint of that diagonal to the opposite corner, giving three triangular pieces. Fitting figures (1), (4) and (5) together along their shared edges, exactly as pictured, reconstructs the square.

• The trio with figures (1), (3) and (4) swaps in figure (3): its stepped, notched outline is not a plain triangle, so it does not match any piece of this three-piece construction.

• The trio with figures (1), (2) and (5) swaps in figure (2): its zig-zag, reflex-angled outline is not a plain triangle, so it does not match any piece of this three-piece construction.

• The trio with figures (1), (2) and (4) carries figure (2)'s non-triangular zig-zag outline and also drops one of the pieces this construction actually needs.

Because figures (1), (4) and (5) are the plain triangles matching this construction, while figures (2) and (3) are not triangles at all, the trio of figures (1), (4) and (5) is the one that fits together to form the complete square.