Are two isosceles triangles never similar?

Two isosceles triangles can be similar if their angles are congruent. Since isosceles triangles have at least two equal sides, they also have two equal angles opposite those sides. If two isosceles triangles have the same angle measures, then they are similar regardless of the lengths of their sides. Therefore, it is incorrect to say that two isosceles triangles are never similar; they can be similar under certain conditions.