Question

topic: properties of angles
progress
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
which two statements are both true?
○ $overleftrightarrow{mn}perpoverleftrightarrow{rs}$ and $overleftrightarrow{mn}perpoverleftrightarrow{pq}$
○ $overleftrightarrow{mn}||overleftrightarrow{pq}$ and $overleftrightarrow{ut}perpoverleftrightarrow{rs}$
○ $overleftrightarrow{pq}perpoverleftrightarrow{tu}$ and $overleftrightarrow{pq}||overleftrightarrow{rs}$
○ $overleftrightarrow{tu}perpoverleftrightarrow{mn}$ and $overleftrightarrow{mn}||overleftrightarrow{pq}$

Explanation:

Step1: Recall angle - related line relationships

Parallel lines are lines that never intersect, and perpendicular lines intersect at a 90 - degree angle.

Step2: Analyze the figure

In the given figure, we can see that $\overleftrightarrow{MN}$ and $\overleftrightarrow{PQ}$ are vertical lines and are parallel to each other ($\overleftrightarrow{MN}\parallel\overleftrightarrow{PQ}$). Also, $\overleftrightarrow{UT}$ is a horizontal line and is perpendicular to $\overleftrightarrow{MN}$ and $\overleftrightarrow{PQ}$, and $\overleftrightarrow{UT}\perp\overleftrightarrow{RS}$.

Answer:

$\overleftrightarrow{MN}\parallel\overleftrightarrow{PQ}$ and $\overleftrightarrow{UT}\perp\overleftrightarrow{RS}$