Parallel Lines: A fundamental portion of constructive Mathematics
Parallel lines are an intriguing part of Mathematics that helps a student in resolving the different complex problems. If one knows the importance of parallel lines, then one should also be familiar with their definition. Parallel lines are two or more lines that do not intersect each other even when extended indefinitely. If two or three parallel lines pass through the same point, they are called ‘parallel’.It is easy to define parallel planes too. Parallel planes cut each other such that they never meet.
To sum up, parallel lines are two or more straight lines that have the same direction and do not cross each other on a plane even though they continue indefinitely in both directions. This is because parallel lines remain parallel all through their course. Also, a line and a plane can be defined as parallel if they do not intersect each other at all.
Parallel lines cut a plane into two separate, non-overlapping regions called ‘parallel planes’. If one has ever used a divider to draw the boundary line between these two regions, then they can imagine that there is a hidden line that separates them. That is true but it cannot be seen because it remains parallel to the plane that contains it. To prove this fact, one can find a straight ray and draw a line on either side. It will be noticed that both of the lines keep going in the same direction forever, even if they are drawn as far as possible. It is due to this property that three or more parallel lines are capable of cutting an infinite plane into several infinite regions.
This article describes the various important properties associated with this crucial topic. It will help in clearing any doubts related to this portion.
Fundamental aspects associated with parallel lines:
- The first and foremost property of parallel lines is that they never meet each other under any condition. Even if they are extended as far as possible in both directions, they will remain parallel to each other. This is the reason why two straight lines are also called ‘parallel’. A plane can be divided into infinite regions by three non-parallel lines. It is due to this property that parallelism is also called ‘lack of crossing’.
- The second property of parallel lines is that they remain the same both vertically and horizontally. This helps a student draw parallel lines on a paper or any other plane without worrying about their direction. For example, lines which are parallel to the x-axis will be parallel to the y-axis. Furthermore, if one can draw two parallel lines on your paper then they can also find their equidistance very easily. They just have to start at one end of the line and keep moving in either direction without turning back. The distance between these two lines will remain the same all through the trip.
- The third property states that only one line can be drawn through a given point. However, it does not mean that a line cannot be extended beyond a point. A line can be extended to infinity in both directions.
This article is an attempt to cover all the important properties that are related to the lines that share a parallel relation between each other. They form a very crucial part of geometry. Students can seek the assistance of Cuemath to solve all the questions related to this important topic. It is an excellent platform that is being recommended by all the teachers because of its efficiency in dealing with problems of any kind. This is the reason why numerous students use this recognized platform.