Final answer:
Only the segments DA and FG are parallel; they are corresponding sides of squares ABCD and EFGH. The other segment pairs given in the options are not parallel to each other.
Step-by-step explanation:
The question asks us to identify parallel segments when given two squares, ABCD and EFGH. In geometry, parallel lines or segments are those that are always the same distance apart and do not meet, no matter how far they are extended. For squares ABCD and EFGH, opposite sides of each square are parallel to each other, and corresponding sides of the two squares will also be parallel.
- A) Segments EA and DG: Not parallel because these are diagonal lines from different squares, which do not run in the same direction.
- B) Segments CF and DA: Not parallel because CF is a side of square EFGH and DA is a side of square ABCD, but they don't correspond to each other, nor are they opposite sides of the same square.
- C) Segments DA and FG: Parallel because DA is a side of square ABCD and FG is the corresponding side of square EFGH.
- D) Segments EH and EA: Not parallel because they represent a side and the extension of a side of square EFGH, which form a perpendicular angle rather than running parallel.
Therefore, the only parallel segments from the options given are DA and FG.