Final answer:
Statement b indicates that the ratios of corresponding sides are equal, which is a necessary condition for triangles to be similar. This statement aligns with the AAA or SAS postulates for triangle similarity. Thus, it is the correct choice indicating similarity between triangles EFI and GFH.
Step-by-step explanation:
The question asks which of the provided statements is true if triangles EFI and GFH are similar. For triangles to be similar, their corresponding sides must be in proportion, and their corresponding angles must be congruent.
Option d, which states that ∠F is congruent to ∠F, is true but does not rely on the triangles being similar as the angle is being compared to itself. It does not provide information about the similarity between triangles EFI and GFH. On the other hand, option b, which states that Segment FH over segment EF is equal to segment HG over segment IE, represents the ratios of corresponding sides in similar triangles. Hence, if the ratios are equal, that's a necessary condition for triangles to be similar according to the AAA (Angle-Angle-Angle) or SAS (Side-Angle-Side) similarity postulates. Therefore, option b is the correct answer.