California Assessment of Student Performance and Progress (CAASPP) Math Practice Exam

What are parallel lines defined as?

1. Lines that intersect at a right angle

2. Lines that lie in the same plane and do not intersect

3. Lines that connect at a point

4. Lines that are always horizontal

The correct answer is: Lines that lie in the same plane and do not intersect

Parallel lines are defined as lines that lie in the same plane and do not intersect. This definition is fundamental in geometry because it captures the essence of what makes two lines parallel — their consistent distance apart and lack of intersection regardless of how far they are extended. The requirement that they lie in the same plane means that both lines exist in a two-dimensional space, allowing for a face-to-face comparison of their behavior regarding intersection. In contrast, other definitions do not accurately represent parallel lines. Lines that intersect at a right angle describe perpendicular lines, which meet at a 90-degree angle. Lines that connect at a point indicate convergence rather than parallelism, as they come together instead of maintaining a uniform distance apart. Finally, stating that lines are always horizontal does not encompass all parallel lines, as parallel lines can run in any direction as long as they never meet. Thus, the correct understanding of parallel lines is based on their inherent property of non-intersection within the same plane.