Parallel Lines

parallel lines
Parallel Lines

The two straight lines which maintain equidistance at all their opposite points and never intersect each other in a plane are defined parallel lines.

Two straight lines are often appeared side by side in a plane. Sometimes, they have some properties commonly. Parallelism is case of two straight lines in which straight lines have four properties commonly.

  1. Equal distance at all their opposite points.
  2. Never intersect each other at any point.
  3. Separate on a plane.
  4. Have same angle.

If two straight lines have the four properties, one straight line is known as a parallel line to another and vice-versa. Therefore, the two straight lines are called parallel lines.

Parallelism of two straight lines is denoted by the symbol () in geometric system.

Example

Equidistance at all opposite points
Equidistance at all opposite points

AB and CD are two straight lines. Let us check the parallelism of these two straight lines.

  1. The straight lines AB and CD both are in same plane.
  2. The angle made by the AB is zero degrees and the angle made by the CD is also zero degrees. In other words, both straight lines maintains same angle in the plane.
  3. The distance from the line AB to line CD is d units. The distance from every point on line AB to exact opposite point on the line CD is same.
  4. Due to equidistance and having same angles, the lines AB and CD do not intersect each other at any point in the plane.

Therefore, AB and CD are parallel lines. The line AB is parallel to the line CD and it is written as AB CD in mathematics. Similarly, the line CD is also parallel to the line AB and it is written as CD AB in mathematics.

Let us look at another example. There are two lines on a plane and they are called lines PQ and RS. Now, check the parallelism of straight lines geometrically.

Equal Angles by the Parallel Lines
Equal Angles by the Parallel Lines
  1. The straight lines PQ and RS are in same plane.
  2. The straight line PQ makes an angle 30° and RS is also making same angle in the plane.
  3. The distance between lines PQ and RS is m units and the distance between them is unique at their all opposite points.
  4. Both lines are making same angle and the distance between them is unique at all the opposite points. Therefore, the lines PQ and RS never intersect each other at any point on the plane.

The straight lines PQ and RS are called parallel lines geometrically. Therefore, it is expressed as PQ RS or RS PQ.

There is one important phenomena involved in the concept of parallelism of straight lines. If the two lines are in same plane and make same angle, the distance between them is same at all the opposite points of both lines and they never either touch or intersect each other at any point in the plane.

In other words, if distance between all opposite points of two lines is same, they make same angles because angles of parallel lines and distance between them have a direct relation geometrically.

So, just check either they are making same angles or they are maintaining equidistance at all the opposite points of the both lines to verify the parallelism of two straight lines in a plane in the geometric system.

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