Question

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? $overleftrightarrow{mn}paralleloverleftrightarrow{pq}$ and $overleftrightarrow{ut}perpoverleftrightarrow{rs}$ $overleftrightarrow{mn}perpoverleftrightarrow{rs}$ and $overleftrightarrow{mn}perpoverleftrightarrow{pq}$ $overleftrightarrow{pq}perpoverleftrightarrow{tu}$ and $overleftrightarrow{pq}paralleloverleftrightarrow{rs}$ $overleftrightarrow{tu}perpoverleftrightarrow{mn}$ and $overleftrightarrow{mn}paralleloverleftrightarrow{pq}$

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 the first option

From the figure, we can see that $\overleftrightarrow{MN}$ and $\overleftrightarrow{PQ}$ are vertical lines, so $\overleftrightarrow{MN}\parallel\overleftrightarrow{PQ}$. Also, $\overleftrightarrow{UT}$ is a horizontal line and $\overleftrightarrow{RS}$ is a non - horizontal and non - vertical line, and they intersect at a right - angle, so $\overleftrightarrow{UT}\perp\overleftrightarrow{RS}$.

Step3: Analyze the second option

$\overleftrightarrow{MN}$ is vertical and $\overleftrightarrow{RS}$ is non - vertical, they are not perpendicular. And $\overleftrightarrow{MN}$ and $\overleftrightarrow{PQ}$ are parallel, not perpendicular.

Step4: Analyze the third option

$\overleftrightarrow{PQ}$ is vertical and $\overleftrightarrow{TU}$ is horizontal, so $\overleftrightarrow{PQ}\perp\overleftrightarrow{TU}$, but $\overleftrightarrow{PQ}$ and $\overleftrightarrow{RS}$ are not parallel.

Step5: Analyze the fourth option

$\overleftrightarrow{TU}$ is horizontal and $\overleftrightarrow{MN}$ is vertical, so $\overleftrightarrow{TU}\perp\overleftrightarrow{MN}$, and $\overleftrightarrow{MN}\parallel\overleftrightarrow{PQ}$ as they are both vertical.

Answer:

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