To understand which statement is true, let's analyze the information given in the question.
The problem states that [tex]\(\overleftrightarrow{P}\)[/tex] and [tex]\(\overleftrightarrow{R}\)[/tex] intersect to form four right angles. This indicates that these lines are perpendicular to each other since they form right angles upon intersection.
Now, let's consider each of the statements:
A. [tex]$\stackrel{\square}{\square S}$[/tex]
This statement is unclear as it doesn't provide any meaningful information or context with the given symbols.
B. [tex]$\overleftrightarrow{\square}$[/tex] and [tex]$\overleftrightarrow{\square S}$[/tex] are skew
Skew lines are lines that do not intersect and are not parallel, typically in three-dimensional space. However, our problem is set in a context where [tex]\(\overleftrightarrow{P}\)[/tex] and [tex]\(\overleftrightarrow{R}\)[/tex] are intersecting lines, and intersecting lines cannot be skew. Therefore, this statement does not apply to the given scenario.
C. [tex]$\overleftrightarrow{Q}$[/tex] and [tex]$\overleftrightarrow{RS}$[/tex] are parallel
There is no information about [tex]\(\overleftrightarrow{Q}\)[/tex] or [tex]$\overleftrightarrow{RS}$[/tex] given in the problem. To determine if they are parallel, we would need a relationship or context connecting these lines to [tex]\(\overleftrightarrow{P}\)[/tex] and [tex]\(\overleftrightarrow{R}\)[/tex]. As such, this cannot be determined from the given information.
D. [tex]$\overleftrightarrow{PQ} = \overleftrightarrow{RS}$[/tex]
This statement suggests that the segments [tex]\(PQ\)[/tex] and [tex]\(RS\)[/tex] are equal, which might imply equal line segments or directions. However, since there is no specific information about these segments or their equality provided, we cannot ascertain this either.
Given the choices and the explanation above, none of the statements can be justified based on the provided information (A lacks context, B is incorrect, and C & D lack necessary information to determine). Thus, none of the statements (A, B, C, or D) seem to be conclusively true under the given circumstances.
