What does the term "similarity ratio" refer to in polygons?

The term "similarity ratio" specifically refers to the ratio of the lengths of corresponding sides of two similar figures. When two polygons are similar, it means that their corresponding angles are equal and the lengths of their corresponding sides are in proportion.

For example, if one triangle has sides that measure 2, 3, and 4, and another triangle has sides measuring 4, 6, and 8, the similarity ratio would be the ratio of any pair of corresponding sides, such as 2:4, which simplifies to 1:2. This consistent ratio between all corresponding sides illustrates that the two figures are indeed similar.

In contrast, the ratio of the areas of two similar figures is related to the square of the similarity ratio and does not directly represent what is meant by "similarity ratio." Similarly, the ratio of the perimeters is equal to the similarity ratio, but since it involves perimeter rather than the more fundamental side lengths, it does not directly define the similarity ratio. The angles of two similar triangles are equal, but their ratio does not represent a numerical relationship as side lengths do.

Thus, the proper definition of the similarity ratio is firmly grounded in the proportionality of the corresponding sides of similar shapes.