What is the primary characteristic of an isometry?

An isometry is a transformation that preserves the geometric properties of figures, specifically the distances between points and the measures of angles. This means that when a figure undergoes an isometric transformation, such as a translation, rotation, or reflection, the resulting figure remains congruent to the original figure.

In this context, preserving distances ensures that the lengths between any two points in the figure remain unchanged, while preserving angles means that the angles formed between lines or segments in the figure also remain constant. These characteristics are fundamental to the definition of isometries, which play a crucial role in geometry, particularly in understanding congruence and symmetry in shapes.

While flipping figures and rotating shapes are types of isometric transformations, they do not encompass the full definition of an isometry. Simply changing sizes does not apply, as it would indicate a dilation rather than an isometry. Thus, the preservation of distances and angles is the key defining feature that accurately describes isometries.