Three distinct coplanar lines a, b, and c satisfying a || b and b || c implies all three lines are parallel. In other words, they never intersect and share the same direction within the same plane. Imagine three train tracks laid parallel to each other; they will never cross each other no matter how far they extend.
Three Coplanar Lines: Parallelism and Intersection
When three distinct coplanar lines a, b, and c satisfy the conditions a || b and b || c, it implies that all three lines are parallel.
Geometric Significance of Parallelism:
Parallelism between a and b: This means that lines a and b never intersect and maintain the same distance throughout their length. Imagine two train tracks laid parallel to each other; they represent lines a and b. No matter how far they extend, they will never cross each other.
Parallelism between b and c: Similarly, lines b and c also maintain a constant distance and never intersect. In the train track analogy, imagine a third track laid parallel to the existing two tracks. All three tracks will run alongside each other indefinitely without ever touching.
Coplanar Lines:
Since all three lines are coplanar, they exist on the same plane. This further reinforces the idea that they cannot intersect, as intersecting lines would require them to be in different planes.
In essence, the parallelism between a and b, as well as between b and c, implies that all three lines are parallel and share the same direction within the same plane.
Image:
The image depicts three parallel lines on a plane. Line b acts as the mediator between lines a and c, demonstrating their shared direction and lack of intersection.
complete question should be :
If three distinct coplanar lines a, b, and c satisfy the conditions a || b and b || c, what relationship does this imply among the lines a, b, and c? Explain the geometric significance of the parallelism between a and b, as well as between b and c, in the context of coplanar lines.