What geometric transformation is used to compare two triangles that are identical in shape and size?

When comparing two triangles that are identical in both shape and size, the appropriate geometric transformation to consider is rotation. This transformation allows one triangle to be turned about a fixed point (which could be a vertex or the centroid) to match the orientation of the other triangle.

In the context of geometry, identical triangles are described as congruent, meaning they have the same angles and side lengths. Therefore, through rotation, it is possible to overlay one triangle over the other without altering their dimensions or proportions.

Translation involves moving a shape from one location to another without changing its orientation, reflection means flipping a shape over a line, and dilation would change the size of the triangles rather than comparing them in their identical states. Thus, rotation is the transformation that accurately represents the process of comparing two congruent triangles while maintaining their original properties.