Question

which statement is true?
○ $overleftrightarrow{uv} perp overleftrightarrow{ab}$ and $overleftrightarrow{wx} || overleftrightarrow{zy}$
○ $overleftrightarrow{ab} || overleftrightarrow{uv}$ and $overleftrightarrow{ab} || overleftrightarrow{wx}$
○ $overleftrightarrow{zy} perp overleftrightarrow{wx}$ and $overleftrightarrow{ab} perp overleftrightarrow{wx}$
○ $overleftrightarrow{uv} perp overleftrightarrow{ab}$ and $overleftrightarrow{uv} || overleftrightarrow{zy}$

Explanation:

Step1: Recall perpendicular and parallel line - segment properties

Perpendicular lines form right - angles (90 degrees), and parallel lines never intersect.

Step2: Analyze the given figure

In the figure, we can observe the orientation of the line - segments. We see that $\overleftrightarrow{UV}$ and $\overleftrightarrow{AB}$ are perpendicular (form right - angles), and $\overleftrightarrow{UV}$ and $\overleftrightarrow{ZY}$ are parallel (they have the same slope and will never intersect).

Answer:

$\overleftrightarrow{UV}\perp\overleftrightarrow{AB}$ and $\overleftrightarrow{UV}\parallel\overleftrightarrow{ZY}$ (corresponding to the last option)