Final answer:
The relationship between line segment FI and other elements can only be established with a diagram or additional information. Possible properties include FI being congruent to AE, perpendicular or parallel to EH, or half the length of EH, each depending on the specific context and geometric figures involved.
Step-by-step explanation:
The question asks about the relationship between line segment FI and other elements such as point E, line EH, and potentially other related geometric figures. Without a diagram or additional information, it's impossible to provide a definitive answer regarding the properties of FI. However, if we consider each statement given: (a) If FI is equal to AE, this could imply that they are congruent segments; (b) If FI is perpendicular to EH, they would form a right angle; (c) If FI is parallel to EH, they would never intersect; (d) If FI is half the length of EH, then FI's length is 0.5 times that of EH. Without further information provided, any of these could potentially be true based on specific conditions within geometric figures. Because we cannot ascertain which statement is correct due to lack of information, it is advised to review the diagram or context provided to determine the correct answer.