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.
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.
and are two straight lines. Let us check the parallelism of these two straight lines.
Therefore, and are parallel lines. The line is parallel to the line and it is written as in mathematics. Similarly, the line is also parallel to the line and it is written as in mathematics.
Let us look at another example. There are two lines on a plane and they are called lines and . Now, check the parallelism of straight lines geometrically.
The straight lines and are called parallel lines geometrically. Therefore, it is expressed as or .
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.