1. The problem asks to list all line segments that are the same length as segment $BG$. 2. From the graph description, segments marked with one line are equal in length. These segments are $BG$, $BF$, $AE$, and $DE$. 3. Therefore, the line segments equal in length to $BG$ are $BF$, $AE$, and $DE$. 4. Among the options given, $AE$ is listed, but $BF$ and $DE$ are not options. So from the options, only $AE$ matches. 5. The other options $AF$, $BE$, $DI$, $EH$, $FG$, $GI$, and $HI$ are not marked as equal to $BG$. Final answer: The line segment equal in length to $BG$ from the options is $AE$.