Question

identify a set of parallel and a set of perpendicular lines in this image. options: \\( overleftrightarrow{ad} parallel overleftrightarrow{bf}, overleftrightarrow{eh} perp overleftrightarrow{cg} \\); \\( overleftrightarrow{eh} parallel overleftrightarrow{cg}, overleftrightarrow{ad} perp overleftrightarrow{cg} \\); \\( overleftrightarrow{bf} parallel overleftrightarrow{cg}, overleftrightarrow{ad} perp overleftrightarrow{bf} \\); \\( overleftrightarrow{ad} parallel overleftrightarrow{cg}, overleftrightarrow{eh} perp overleftrightarrow{bf} \\)

Explanation:

1. First, identify parallel lines: Lines that run in the same direction and never intersect. $\overleftrightarrow{BF}$ and $\overleftrightarrow{CG}$ are both vertical, so they are parallel.
2. Then, identify perpendicular lines: Lines that intersect at a right angle (marked by the square symbol). $\overleftrightarrow{AD}$ and $\overleftrightarrow{BF}$ intersect at a right angle, so they are perpendicular.
3. Match this pair to the given options.

Answer:

$\boldsymbol{\overleftrightarrow{BF} \parallel \overleftrightarrow{CG}, \overleftrightarrow{AD} \perp \overleftrightarrow{BF}}$