What is the relationship between corresponding sides, altitudes, and medians in similar triangles?

The ratio of their lengths is the same.

Similarity can be defined through a concept of scaling (see Unizor - "Geometry - Similarity").

Accordingly, all linear elements (sides, , medians, radiuses of inscribed and circumscribed circles etc.) of one triangle are scaled by the same scaling factor to be congruent to corresponding elements of another triangle. This scaling factor is the ratio between the lengths of all corresponding elements and is the same for all elements.