Question

question 2
which statement is true?
○ $overleftrightarrow{ab}||overleftrightarrow{uv}$ and $overleftrightarrow{ab}||overleftrightarrow{wx}$
○ $overleftrightarrow{uv}perpoverleftrightarrow{ab}$ and $overleftrightarrow{uv}||overleftrightarrow{zy}$
○ $overleftrightarrow{zy}perpoverleftrightarrow{wx}$ and $overleftrightarrow{ab}perpoverleftrightarrow{wx}$
○ $overleftrightarrow{uv}perpoverleftrightarrow{ab}$ and $overleftrightarrow{wx}||overleftrightarrow{zy}$

Explanation:

Step1: Recall parallel and perpendicular line - segment properties

Parallel line - segments never intersect and perpendicular line - segments intersect at a 90 - degree angle.

Step2: Analyze each option

• Option 1: $\overrightarrow{AB}\parallel\overrightarrow{UV}$ and $\overrightarrow{AB}\parallel\overrightarrow{WX}$: From the figure, we can see that $\overrightarrow{AB}$ is not parallel to $\overrightarrow{WX}$.
• Option 2: $\overrightarrow{UV}\perp\overrightarrow{AB}$ and $\overrightarrow{UV}\parallel\overrightarrow{ZY}$: $\overrightarrow{UV}$ and $\overrightarrow{AB}$ are perpendicular as they intersect at a right - angle, and $\overrightarrow{UV}$ and $\overrightarrow{ZY}$ are parallel since they are both horizontal.
• Option 3: $\overrightarrow{ZY}\perp\overrightarrow{WX}$ and $\overrightarrow{AB}\perp\overrightarrow{WX}$: $\overrightarrow{ZY}$ is not perpendicular to $\overrightarrow{WX}$.
• Option 4: $\overrightarrow{UV}\perp\overrightarrow{AB}$ is correct, but $\overrightarrow{WX}\parallel\overrightarrow{ZY}$ is incorrect as they are perpendicular.

Answer:

$\overrightarrow{UV}\perp\overrightarrow{AB}$ and $\overrightarrow{UV}\parallel\overrightarrow{ZY}$