Final answer:
To determine which statement is true only if triangles EFI and GFH are similar, we need to examine each statement. The correct statement is c) Triangles EFI and GFH have congruent sides.
Step-by-step explanation:
To determine which statement is true only if triangles EFI and GFH are similar, let's examine each option:
a) ∠E ≅ ∠G: This statement is true for all similar triangles. So, if ∠E ≅ ∠G, it does not necessarily mean that triangles EFI and GFH are similar. Therefore, this statement is not true only if triangles EFI and GFH are similar.
b) Segments EG and IH intersect at point F: The intersection of the two segments does not determine triangle similarity. So, this statement is not true only if triangles EFI and GFH are similar.
c) Triangles EFI and GFH have congruent sides: This statement is true only if triangles EFI and GFH are similar. Similar triangles have corresponding sides that are proportional in length. Therefore, this statement is true only if triangles EFI and GFH are similar.
d) None of the above: This statement is not true since option c) is true. So, the correct answer is c) Triangles EFI and GFH have congruent sides.