Can the figure below tessellate a plane? Explain your answer.

Question

A shape is formed by cutting out a smaller semicircle from a larger semicircle. The remaining closed figure resembling an arch is shown.

Answer 1

No, this figure cannot tessellate a plane. A shape can only tessellate a plane if it can be translated and rotated to fit together with identical copies of itself without leaving any gaps or overlaps. Since this arch-shaped figure has a curved edge, it cannot be translated and rotated to fit perfectly with identical copies of itself without leaving gaps or overlaps. Therefore, it cannot tessellate a plane.