Which of the following conditions is NOT required for triangles to be similar?

In the context of triangle similarity, two triangles are considered similar if they have the same shape, regardless of their size. For triangles to be similar, specific conditions related to their angles and side lengths must be met.

The condition stating that all angles must match up is essential for similarity. If two triangles have all corresponding angles equal, then they are similar by the Angle-Angle (AA) criterion.

The condition that all three sides must be equal in length is not a requirement for similarity. Instead, it's a characteristic of congruent triangles, which are a special case of similarity. While congruent triangles are also similar (since they have equal angles and sides), similarity does not necessitate that all corresponding sides be equal; they only need to be proportional.

Having two sides proportional with the angle between them being the same is sufficient for establishing the similarity of triangles, aligning with the Side-Angle-Side (SAS) similarity criterion.

Lastly, for all three sides to be proportional is a condition that guarantees similarity, corresponding to the Side-Side-Side (SSS) similarity criterion.

Thus, the condition of having all three sides equal in length is the one that is not required for triangles to be similar, making it the correct choice