Question

topic: properties of angles
progress:
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
identify a set of parallel and a set of perpendicular lines in this image.
\\( overleftrightarrow{bf} \parallel \overleftrightarrow{cg}, \overleftrightarrow{ad} \perp \overleftrightarrow{eh} \\)
\\( overleftrightarrow{bf} \parallel \overleftrightarrow{cg}, \overleftrightarrow{bf} \perp \overleftrightarrow{cg} \\)
\\( overleftrightarrow{ad} \parallel \overleftrightarrow{eh}, \overleftrightarrow{eh} \perp \overleftrightarrow{bf} \\)
\\( overleftrightarrow{ad} \parallel \overleftrightarrow{eh}, \overleftrightarrow{bf} \perp \overleftrightarrow{cg} \\)

Explanation:

Step1: Recall line - relationship definitions

Parallel lines never intersect, and perpendicular lines intersect at right - angles (90 degrees).

Step2: Examine the given lines

In the image, $\overleftrightarrow{BF}$ and $\overleftrightarrow{CG}$ are vertical lines and do not intersect, so $\overleftrightarrow{BF}\parallel\overleftrightarrow{CG}$. Also, $\overleftrightarrow{AD}$ and $\overleftrightarrow{EH}$ are horizontal lines and do not intersect, so $\overleftrightarrow{AD}\parallel\overleftrightarrow{EH}$. And $\overleftrightarrow{AD}$ is perpendicular to $\overleftrightarrow{BF}$, $\overleftrightarrow{AD}$ is perpendicular to $\overleftrightarrow{CG}$, $\overleftrightarrow{EH}$ is perpendicular to $\overleftrightarrow{BF}$, and $\overleftrightarrow{EH}$ is perpendicular to $\overleftrightarrow{CG}$.

Answer:

$\overleftrightarrow{BF}\parallel\overleftrightarrow{CG}$, $\overleftrightarrow{AD}\perp\overleftrightarrow{EH}$ (the first option)