Question

2
if $overline{pq}$ and $overline{rs}$ are coplanar and do not intersect, which of the following statements are true?
check all that apply.
□ $overline{pq}$ and $overline{rs}$ are parallel
□ $overline{pq}$ and $overline{rs}$ intersect at a single point
□ $overline{pq}paralleloverline{rs}$
□ $overline{pq}$ and $overline{rs}$ do not intersect
□ $overline{pq}perpoverline{rs}$
□ $overline{pq}$ and $overline{rs}$ are coplanar

Explanation:

Step1: Recall parallel - line definition

In a plane, non - intersecting lines are parallel.

Step2: Analyze each statement

Given that $\overline{PQ}$ and $\overline{RS}$ are coplanar and do not intersect:

• “$\overline{PQ}$ and $\overline{RS}$ are parallel”: By the definition of parallel lines in a plane (coplanar and non - intersecting), this is true.
• “$\overline{PQ}$ and $\overline{RS}$ intersect at a single point”: Given they do not intersect, this is false.
• “$\overline{PQ}\parallel\overline{RS}$”: This is just another way of saying they are parallel, so it is true.
• “$\overline{PQ}$ and $\overline{RS}$ do not intersect”: Given in the problem statement, this is true.
• “$\overline{PQ}\perp\overline{RS}$”: Perpendicular lines intersect at a right - angle, but they do not intersect, so this is false.
• “$\overline{PQ}$ and $\overline{RS}$ are coplanar”: Given in the problem statement, this is true.

Answer:

$\overline{PQ}$ and $\overline{RS}$ are parallel, $\overline{PQ}\parallel\overline{RS}$, $\overline{PQ}$ and $\overline{RS}$ do not intersect, $\overline{PQ}$ and $\overline{RS}$ are coplanar.