Final answer:
The only statement that confirms the similarity of triangles EFI and GFH is option (b), which represents the proportionality of corresponding sides in similar triangles, a defining characteristic of similarity.
Step-by-step explanation:
The question you're asking is about determining the condition that confirms the similarity of triangles EFI and GFH. Similar triangles have corresponding angles that are congruent and corresponding sides in proportion. Given the choices, the correct statement that would verify that triangles EFI and GFH are similar is (b) Segment EI / Segment FI = Segment GH / Segment FE.
Choice (a) Segment FI = Segment FH does not necessarily imply similarity, as it only states that these two segments are congruent. Similar triangles can have sides of different lengths, but the ratios of the lengths of corresponding sides will be equal. Choice (c) ∠E ≅ ∠G suggests that these angles are congruent, which can be a result of similarity; however, for triangles to be similar, all corresponding angles need to be congruent, not just a single pair. Choice (d) Segments EG and IH intersect at point F is irrelevant to the condition for the similarity of two triangles.