Triangles A B C and A B F are congruent. Triangle A B C is reflected across line B A to form triangle A B F.

To map triangle \( \triangle ABC \) to triangle \( \triangle ABF \), you need to consider the given transformations and the description of the triangles.

Since it is stated that triangle \( \triangle ABC \) is reflected across line \( BA \) to form triangle \( \triangle ABF \), the transformation that directly accomplishes this is a reflection.

The correct rigid transformation that would map \( \triangle ABC \) to \( \triangle ABF \) is:

A reflection across the line containing BA.

So, the answer is: a reflection across the line containing BA.