To determine which pieces could be used four times individually to form a square, we must analyze each piece's shape and symmetry. The rules allow rotation and flipping, but they cannot overlap. This means that the piece should, when used four times, create a continuous, equal-sided quadrilateral—namely a square. Let's evaluate each option:
Piece 1: This piece can form a square because when put together in all four orientations (each side of the square), the corners and edges align perfectly, forming an enclosed square shape without overlapping.
Piece 2: Similar to Piece 1, this shape can be manipulated through rotation and flipping such that the edges align without overlapping, thus forming a complete square when used four times.
Piece 3: This piece cannot form a square when used four times because its geometrical structure and asymmetrical side lengths do not allow it to connect all corners seamlessly to form a closed square without gaps or overlaps.
Piece 4: As with Pieces 1 and 2, Piece 4 can also form a square through proper rotation and flipping. Its edges and angles are compatible with each other to completely and symmetrically fill in a square shape.
Therefore, Pieces 1, 2, and 4 can each be used four times to form a square.
