1. **Problem Statement:** Pentagon EFGHI is rotated 180° clockwise about point I to form pentagon E'F'G'H'I'. We need to determine which line segment is parallel to TH'. 2. **Understanding Rotation:** A 180° rotation about a point means every point is rotated half a turn around that point. The image of a point P after rotation about I is such that I is the midpoint of segment PP'. 3. **Key Insight:** Since the rotation is about point I, point I remains fixed. The segment TH' connects point T (which is not a vertex of the pentagon, but presumably a point related to the figure) to H' (the image of H after rotation). 4. **Analyzing the Options:** - a) EI: segment from E to I - b) GH: segment from G to H - c) TE': segment from T to E' (image of E after rotation) 5. **Rotation Properties:** - The segment GH will rotate to G'H'. - The segment EI will rotate to E'I'. - Since I is the center, EI and E'I' are collinear and opposite directions. 6. **Determining Parallelism:** - TH' is a segment involving H' (rotated H) and T. - TE' involves E' (rotated E) and T. 7. **Conclusion:** Because rotation preserves angles and parallelism, the segment TE' will be parallel to TH' after rotation. **Final answer:** c) TE'