Question

identify a set of parallel and a set of perpendicular lines in this image.
○ $overleftrightarrow{bf}paralleloverleftrightarrow{cg}$, $overleftrightarrow{ad}perpoverleftrightarrow{bf}$
○ $overleftrightarrow{ad}paralleloverleftrightarrow{cg}$, $overleftrightarrow{eh}perpoverleftrightarrow{bf}$
○ $overleftrightarrow{ad}paralleloverleftrightarrow{bf}$, $overleftrightarrow{eh}perpoverleftrightarrow{cg}$
○ $overleftrightarrow{eh}paralleloverleftrightarrow{cg}$, $overleftrightarrow{ad}perpoverleftrightarrow{cg}$

Explanation:

Step1: Recall parallel - line definition

Parallel lines are lines that never intersect and have the same slope. In the given figure, we can observe the orientation of the lines. $\overleftrightarrow{AD}$ and $\overleftrightarrow{EH}$ are vertical lines and they do not intersect, so $\overleftrightarrow{AD}\parallel\overleftrightarrow{EH}$. Also, $\overleftrightarrow{BF}$ and $\overleftrightarrow{CG}$ are horizontal lines and do not intersect, so $\overleftrightarrow{BF}\parallel\overleftrightarrow{CG}$.

Step2: Recall perpendicular - line definition

Perpendicular lines intersect at a right - angle (90 degrees). We can see that vertical lines like $\overleftrightarrow{AD}$ and $\overleftrightarrow{EH}$ are perpendicular to horizontal lines like $\overleftrightarrow{BF}$ and $\overleftrightarrow{CG}$. For example, $\overleftrightarrow{AD}\perp\overleftrightarrow{BF}$ and $\overleftrightarrow{EH}\perp\overleftrightarrow{CG}$.

Answer:

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