Can transformation properties change for figures on a non-Euclidean plane?

The correct choice indicates that transformation properties may indeed differ in non-Euclidean planes due to the curvature of the surface. In Euclidean geometry, the rules governing transformations such as translations, rotations, and reflections hold true consistently across flat surfaces. However, in non-Euclidean geometries, such as hyperbolic or spherical geometries, the inherent curvature of the plane alters the relationships and properties of shapes.

For instance, in spherical geometry, the sum of angles in a triangle can exceed 180 degrees, and parallel lines can converge or diverge differently than they would in Euclidean space. These differences can significantly impact how transformations are applied and how figures are perceived in relation to one another. Thus, transformation properties must adapt to account for the unique rules imposed by the curvature of the non-Euclidean environment.

Understanding this distinction is crucial for working with figures in various geometric contexts, as it highlights the flexibility of transformation rules and the necessity of considering the underlying structure of the space in which the figures exist. This is why the statement that they may differ due to curvature is accurate and reflects the foundational principles of geometry beyond Euclidean frameworks.