Question

identify a set of parallel lines and a set of perpendicular lines in this image.
ac || bd, ab ⊥ ef
ab || cd, ab ⊥ cd
ab || cd, ab ⊥ ef
ad || cb, ab ⊥ ef

Explanation:

Step1: Recall parallel and perpendicular definitions

Parallel lines are lines that never intersect. Perpendicular lines intersect at a right - angle ($90^{\circ}$).

Step2: Analyze each option

• Option1: $\overleftrightarrow{AC}\parallel\overleftrightarrow{BD}$ is wrong as they are the same line (vertical). $\overleftrightarrow{AB}\perp\overleftrightarrow{EF}$ is correct, but the first part is wrong.
• Option2: $\overleftrightarrow{AB}\parallel\overleftrightarrow{CD}$ is wrong as they are the same line (vertical). $\overleftrightarrow{AB}\perp\overleftrightarrow{CD}$ is wrong (they are the same line).
• Option3: $\overleftrightarrow{AB}\parallel\overleftrightarrow{CD}$ (both vertical, so parallel). $\overleftrightarrow{AB}\perp\overleftrightarrow{EF}$ (intersect at right - angle). This option is correct.
• Option4: $\overleftrightarrow{AD}\parallel\overleftrightarrow{CB}$ is wrong as they are the same line (vertical). $\overleftrightarrow{AB}\perp\overleftrightarrow{EF}$ is correct, but the first part is wrong.

Answer:

$\overleftrightarrow{AB}\parallel\overleftrightarrow{CD},\overleftrightarrow{AB}\perp\overleftrightarrow{EF}$ (Option3)