What can be said about the lengths of corresponding line segments in isometry?

In isometry, the defining characteristic is that it preserves distances between points. This means that when you perform an isometric transformation—such as translation, rotation, or reflection—each point of a figure moves to a new position, but the distance between any two points remains unchanged. Therefore, the lengths of corresponding line segments before and after the transformation are exactly the same.

This preservation of length is a fundamental property of isometric transformations; the figures may appear in different positions or orientations, but the size and shape remain consistent. Since all distances are maintained during an isometry, the correct statement highlights that the lengths of corresponding line segments remain constant.