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

Explanation:

Step1: Recall the definitions of parallel and perpendicular lines

Parallel lines are lines that never intersect and have the same slope (in coordinate - plane terms, or in geometric terms, they maintain a constant distance apart). Perpendicular lines intersect at a right angle (\(90^{\circ}\)).

Step2: Analyze each option

• Option 1:
• \(\overleftrightarrow{MN}\perp\overleftrightarrow{RS}\): \(\overleftrightarrow{MN}\) is a vertical line (assuming the standard orientation of the coordinate - like system in the figure), and \(\overleftrightarrow{RS}\) is a non - vertical line. They are not perpendicular.
• \(\overleftrightarrow{MN}\perp\overleftrightarrow{PQ}\): \(\overleftrightarrow{MN}\) and \(\overleftrightarrow{PQ}\) are both vertical lines. Vertical lines are parallel (\(\overleftrightarrow{MN}\parallel\overleftrightarrow{PQ}\)), not perpendicular.
• Option 2:
• \(\overleftrightarrow{TU}\perp\overleftrightarrow{MN}\): \(\overleftrightarrow{TU}\) is a horizontal line and \(\overleftrightarrow{MN}\) is a vertical line. Horizontal and vertical lines are perpendicular.
• \(\overleftrightarrow{MN}\parallel\overleftrightarrow{PQ}\): \(\overleftrightarrow{MN}\) and \(\overleftrightarrow{PQ}\) are both vertical lines. Vertical lines are parallel.
• Option 3:
• \(\overleftrightarrow{PQ}\perp\overleftrightarrow{TU}\): \(\overleftrightarrow{PQ}\) is vertical and \(\overleftrightarrow{TU}\) is horizontal, so \(\overleftrightarrow{PQ}\perp\overleftrightarrow{TU}\) is true.
• \(\overleftrightarrow{PQ}\parallel\overleftrightarrow{RS}\): \(\overleftrightarrow{PQ}\) is vertical and \(\overleftrightarrow{RS}\) is non - vertical. They are not parallel.
• Option 4:
• \(\overleftrightarrow{MN}\parallel\overleftrightarrow{PQ}\): True (both vertical).
• \(\overleftrightarrow{UT}\perp\overleftrightarrow{RS}\): \(\overleftrightarrow{UT}\) is horizontal and \(\overleftrightarrow{RS}\) is non - vertical. They are not perpendicular.

Answer:

\(\overleftrightarrow{TU}\perp\overleftrightarrow{MN}\) and \(\overleftrightarrow{MN}\parallel\overleftrightarrow{PQ}\) (the second option)