Final answer:
In addressing which statement is true if triangles EFI and GFH are similar, the most relevant statement would be option d), stating that lines EI and HG are parallel, since it suggests similarity through the Angle-Angle criterion. However, the exact determination of similarity requires information about the corresponding sides and angles.
Step-by-step explanation:
The question is aimed at understanding the properties that would be true if two triangles EFI and GFH are similar. When two triangles are similar, their corresponding sides are in proportion and their corresponding angles are equal. This definition helps in determining the accuracy of the given statements.
For example, if it's stated that segment FI is to segment FH as 2 is to 3 (c), this could imply that the triangles are similar if the other sides are also in the same proportion and all corresponding angles are equal. However, for triangles to be similar, it is not required that the line segments EG and HI intersect at point F (a), nor is it necessary for a line to intersect both triangles at a single point (b). The statement about lines EI and HG being parallel (d) could hint at triangles being similar by the Angle-Angle (AA) criterion if the parallel lines create corresponding angles in each triangle.
Without specific information about the angles or other sides, it is challenging to confirm the similarity. Thus, if one has to choose, option d lines EI and HG are parallel, seems the most directly related to triangles being similar, following the AA criterion. Yet, the exact answer would depend on other geometrical aspects of triangles EFI and GFH which are not provided in the question.