Question

according to the figure, which statement is correct? a $overleftrightarrow{af}$ and $overleftrightarrow{be}$ appear to be parallel. b $overleftrightarrow{be}$ and $overleftrightarrow{cd}$ appear to be perpendicular. c $overleftrightarrow{ac}$ and $overleftrightarrow{af}$ appear to be perpendicular. d $overleftrightarrow{be}$ and $overleftrightarrow{fd}$ appear to be perpendicular.

Explanation:

Step1: Recall parallel and perpendicular lines

Parallel lines never intersect, perpendicular lines intersect at 90 - degree angles.

Step2: Analyze Option A

$\overleftrightarrow{AF}$ and $\overleftrightarrow{BE}$ do not intersect and have the same "slant", so they appear parallel.

Step3: Analyze Option B

$\overleftrightarrow{BE}$ and $\overleftrightarrow{CD}$ are parallel as they are both vertical, not perpendicular.

Step4: Analyze Option C

$\overleftrightarrow{AC}$ is horizontal and $\overleftrightarrow{AF}$ is slanted, they are not perpendicular.

Step5: Analyze Option D

$\overleftrightarrow{BE}$ is vertical and $\overleftrightarrow{FD}$ is horizontal, they are parallel, not perpendicular.

Answer:

A. $\overleftrightarrow{AF}$ and $\overleftrightarrow{BE}$ appear to be parallel.