Final answer:
To prove congruence by SAS, we need matching sides and the included angle. Statements BA=ED and AC=DF suggest equal sides, but without the included angle, we cannot determine congruence. Therefore, more information is needed to apply the SAS postulate.
Step-by-step explanation:
The question you've asked is related to proving that two triangles are congruent using the Side-Angle-Side (SAS) postulate in geometry. To prove congruence by SAS, we need to show that two sides and the angle between them in one triangle are congruent to two sides and the angle between them in the other triangle.
If a sequence of rigid transformations (rotation, reflection, translation) is applied to triangle ABC resulting in triangle DEF, and we want to show that those triangles are congruent by SAS, we need to demonstrate that corresponding sides and the included angle are equal. Statements (a) BA=ED and (d) BA=ED are identical and they suggest that one pair of corresponding sides is equal. But to demonstrate SAS congruence, we must also prove that a pair of corresponding angles and the other side adjacent to this angle are equal.
Statement (b) AC=DF provides a second pair of corresponding sides. But to complete the SAS, we need to ensure that the angle between BA and AC in triangle ABC is congruent to the angle between ED and DF in triangle DEF.
Therefore, the correct statement to prove the triangles are congruent by SAS would require both a specification of equal corresponding sides and the included angle. None of the statements provided are sufficient on their own to prove congruence by SAS.