the image of $ \triangle abc $ after a reflection across $ \overleftrightarrow{eg} $ is $ \triangle abc $.
which statement is true about point $ f $?
$ \bigcirc $ $ f $ is the midpoint of $ \overline{aa} $ because $ \overleftrightarrow{eg} $ bisects $ \overline{aa} $.
$ \bigcirc $ $ f $ is the midpoint of $ \overline{eg} $ because $ \overline{aa} $ bisects $ \overline{eg} $.
$ \bigcirc $ $ f $ is the midpoint of $ \overline{aa} $ because $ \overline{aa} $ bisects $ \overline{eg} $.
$ \bigcirc $ $ f $ is the midpoint of $ \overline{eg} $ because $ \overleftrightarrow{eg} $ bisects $ \overline{aa} $.

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# Brief Explanations:
When a figure is reflected across a line, the line of reflection is the perpendicular bisector of the segment joining a point and its image. Here, line $ \overline{TG}$ is the line of reflection. For point $A$ and its image $A'$, line $ \overline{TG}$ bisects $ \overline{AA'}$. The mid - point of a segment is the point that divides the segment into two equal parts. Since $ \overline{TG}$ bisects $ \overline{AA'}$, the point $F$ (where $ \overline{AA'}$ and $ \overline{TG}$ intersect) is the mid - point of $ \overline{AA'}$.

# Answer:
F is the midpoint of $ \overline{AA'}$ because $ \overline{TG}$ bisects $ \overline{AA'}$ (the first option).

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