Parallel lines


To speak of parallel lines we must understand that a straight line is a succession of forms infinite of points which are located all in a same direction , succession is characterized as so continuous and indefinite , is why we say that a straight it has neither beginning nor end. Then parallel lines are two lines that have no point in common , nor are coincident. Two lines that are located in a plane are parallel if they are either one and the same line or, on the contrary, if they are not sharing any point in common. Similarly, in space they can be parallel if they are one and the same plane or if they are not sharing any point .


What are parallel lines?

Parallel lines are the lines that lie within a same plane and having the same slope and exhibiting no point in common , that is not cross or touch nor intersect in their extensions .

  • Definition
  • features
  • Properties
  • Distance between two parallel lines
  • Objects with parallel lines
  • Solved exercises
  • Examples


In order to explain and clarify the meaning of parallel lines, we must first give a brief explanation about the concept of what a line is ; and we can say then that a line is a consecutive series of points , which are all located in the same direction , and which have as characteristics being continuous and infinite , in other words, that they have no beginning or end.


Parallel lines are the type of line that maintains a certain distance from each other, and although they have the ability to extend their trajectory to infinity, they can never meet or touch at any point ; In other words, we understand by the name of parallel lines those lines that are located within the same plane , and that do not also have any common point between them and show the same slope, this means that they cannot touch or cross , not even its extensionsthey can cross between them, a clear example of the parallel lines that we see daily are the train tracks.


The main characteristics of parallel lines are the following:

  • Are always at the same distance but never will touch each other .
  • Parallel lines or lines are always pointing in the same direction .
  • When the parallel lines intersect with another line, which is known as Transversal , it can be seen that the angles are equal.
  • Parallel lines have a pair of corresponding and equal angles .
  • They have a pair of alternate interior angles of equal measure.


Among the properties that we can mention with respect to a parallel line are:

  • It has symmetry , which means that one line is parallel to another, for this reason, it will be parallel to the first .
  • They are reflective because every line is parallel to itself.
  • Parallel lines have a corollary , all parallel lines have the same direction; corollary of the transitive p, two parallel lines with respect to a third will be parallel to each other; and transitive , if a line is parallel to another and at the same time to a third, then the first will be parallel to the third line.
  • They have a perpendicularity relationship which occurs between two lines, where at a certain point the lines are divided resulting in four right angles , in other words four angles with a measure of 90 ° each; We can see this, for example, at the intersection of two streets where you can clearly see the four right angles that are formed at each corner.

Distance between two parallel lines

The distance that exists between two lines that are parallel is the same as the distance that exists from any point on one of the lines to the other line .

Objects with parallel lines

Some of the objects in which we can find parallel lines are:

  • On a wall, at the junction of its corners.
  • In a window with double division (in the shape of a cross).
  • In the corner of a door.
  • It could be the junction of a utility pole with the floor.
  • The diagonal of a pizza box.
  • The train lines.
  • At a street intersection.

Solved exercises

Some examples of exercises already solved with respect to parallel lines are the following:

Determine the value of t so that the following lines are parallel:

r: 3x – 4y + 12 = 0

s: tx + 8y – 15 = 0

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