What ratio represents the relationship between similar figures?

The relationship between similar figures is fundamentally based on the proportionality of their corresponding dimensions. When two figures are similar, all corresponding lengths (such as sides, heights, and bases) are proportional to each other. This means that if you take the lengths of corresponding sides, their ratios will be consistent across the shape, regardless of their actual size.

For example, if one triangle is a scaled version of another, the sides of the smaller triangle will be in a fixed ratio to the sides of the larger triangle. This ratio is known as the scale factor, and it plays a crucial role in determining other properties of the figures.

While the ratios of circumferences or diagonals could relate to the figures, they are derived from the ratios of corresponding sides. The areas of similar figures are also related to the square of the ratio of the lengths of corresponding sides. Therefore, the most direct and straightforward representation of the relationship between similar figures is through the ratio of the lengths of corresponding sides.