To solve this question, let's break down the information and requirements step-by-step.
1. Understanding the problem:
- We are given that [tex]$\overleftrightarrow{P Q}$[/tex] and [tex]$\overleftrightarrow{R S}$[/tex] intersect.
- The intersection forms four right angles.
2. Analyzing the results of the intersection:
- When two lines intersect to form four right angles, it implies that each angle formed at the intersection is 90 degrees.
- This specific formation of four right angles means that the two lines are perpendicular to each other.
3. Evaluating the given statements:
- Statement A: [tex]$\overrightarrow{P Q}=\overleftrightarrow{R S}$[/tex]
- This statement suggests that [tex]$\overleftrightarrow{P Q}$[/tex] and [tex]$\overleftrightarrow{R S}$[/tex] are essentially the same line. However, if they intersect at right angles, they cannot be the same line.
- Statement B: [tex]$\overleftrightarrow{P Q} \perp \overleftrightarrow{R S}$[/tex]
- This statement suggests that [tex]$\overleftrightarrow{P Q}$[/tex] is perpendicular to [tex]$\overleftrightarrow{R S}$[/tex]. Given that intersecting at four right angles means they are perpendicular, this statement is true.
- Statement C: [tex]$\overrightarrow{P Q}$[/tex] and [tex]$\overparen{R S}$[/tex] are skew
- Skew lines are lines that do not intersect and are not parallel. Since [tex]$\overleftrightarrow{P Q}$[/tex] and [tex]$\overleftrightarrow{R S}$[/tex] do intersect, this statement is false.
- Statement D: [tex]$\overrightarrow{P Q}$[/tex] and [tex]$\overparen{R S}$[/tex] are parallel
- If two lines are parallel, they never intersect. Since it is given that [tex]$\overleftrightarrow{P Q}$[/tex] and [tex]$\overleftrightarrow{R S}$[/tex] do intersect, this statement is also false.
4. Conclusion:
- The correct statement based on the problem is that the lines are perpendicular.
Therefore, the true statement is:
B. [tex]$\overleftrightarrow{P Q} \perp \overleftrightarrow{R S}$[/tex]
