Two distinct coplanar lines that do not intersect are known as __ lines.
The Correct Answer and Explanation is:
Two distinct coplanar lines that do not intersect are known as parallel lines.
Explanation:
Parallel lines are lines that are in the same plane (i.e., they are coplanar) and run in the same direction. The key feature of parallel lines is that they do not meet, no matter how far they are extended. They are equidistant from each other at every point, which means the distance between them remains constant.
This is in contrast to lines that are non-coplanar (skew lines), which don’t lie in the same plane, and therefore cannot be parallel. Also, two coplanar lines that do intersect are called intersecting lines, not parallel lines.
Mathematically, if two lines have the same slope, they are parallel in a two-dimensional Cartesian coordinate system. For example, the lines represented by the equations y=2x+3y = 2x + 3y=2x+3 and y=2x−4y = 2x – 4y=2x−4 are parallel because they have the same slope of 2 but different y-intercepts. Thus, they will never meet, and they remain equidistant.
On the other hand, if the slopes of two lines are different, they will eventually intersect at a point, and therefore cannot be parallel. In three-dimensional space, parallel lines must also not be skew lines, which are lines that do not lie on the same plane and do not intersect.
Parallel lines are often a fundamental concept in geometry and are essential when analyzing various properties of shapes, angles, and distances.
