What do similar triangles have in common regarding their corresponding sides?

Similar triangles share a fundamental characteristic in that their corresponding sides are proportional. This means that the lengths of the sides of one triangle are in the same ratio to the lengths of the corresponding sides of the other triangle. For example, if one triangle has sides of lengths 4, 6, and 8, then a similar triangle might have sides of lengths 2, 3, and 4, maintaining the same proportional relationship (2:4, 3:6, and 4:8 all simplify to the same ratio).

This property is crucial in geometry as it allows for the comparison of triangles regardless of their size. The angles of the triangles are also congruent, which further supports the idea of similarity beyond just the lengths of the sides. This proportionality is what distinguishes similar triangles from congruent triangles, which do require all sides to be equal in length.

The idea of corresponding sides being different lengths does not relate to similarity; instead, it's the consistent ratio that defines similarity. The option stating that all sides must be equal in length pertains to congruency, not similarity. Lastly, stating that the ratio of their corresponding sides is always 1 implies that the triangles are identical in size, which contradicts the concept of similarity