Final answer:
Residents of Flatland could distinguish shapes by observing light reflections and shadows, physically feeling the outlines, or by noting movement patterns and social behaviors linked to specific shapes.
Step-by-step explanation:
Inhabitants of “Flatland”, a conceptual two-dimensional world, could recognize each other's shape through various methods. One way would be by sensing the angle at which another being reflects light or casts a shadow, as different shapes would modify these aspects uniquely. A second method might involve physical perception; as inhabitants move around, they can palpate the edges and vertices of others, distinguishing shapes by feeling.
Finally, since behavior in Flatland could be indicative of shape (as experienced in Edwin A. Abbott's novel “Flatland”), observation of movement patterns and social interactions could also serve as cues for recognizing shapes. For example, circles might move smoothly, while polygons may exhibit more rigid motions.