A Straight it is an infinite succession of points, all located in the same direction, while that succession is characterized by being continuous and indefinite, therefore, a line has neither beginning nor end; together with the plane and the point, the line is one of the fundamental geometric entities. And parallel is an adjective that is used to refer to something similar, corresponding or that has been developed at the same time.
It should be pointed out by the way that the lines will differ so much from the rays that have a beginning but no end, and from the segments that begin and end at certain points.
Then the parallel lines are those straight lines that are in the same plane, have the same slope and do not have any common point, this means that they do not cross, or touch and they will not even cross their extensions. One of the most popular examples is that of a train track.
The properties that they have are: thoughtful (every line is parallel to itself), symmetrical (if one line is parallel to another, that one will be parallel to the first one), transitive (if a line is parallel to another and this in turn is parallel to a third, the first will be parallel to the third line), corollary of transitive p (two lines parallel to a third will be parallel to each other) and corollary (all parallel lines have the same direction).
Meanwhile, the theorems related to parallel lines tell us: that in a plane, two lines perpendicular to a third will be parallel to each other; through a point outside a line, a point parallel to that line will always pass; and if a line cuts one of two parallels, it will also cut the other, always speaking in a plane.
The drawing of the parallel lines can be carried out with a ruler and square or with a ruler and compass.
The study of lines through history
Euclid was a well-known mathematician during classical Greece. and for all his contributions is that he is considered as a father of geometry. He lived between 325 and 265 BC, in Alexandria, and together with a team of colleagues who knew how to lead wrote the work of The elements, which is considered one of the most popular scientific works in the world and that brings together a good part of the basic knowledge of geometry that has been taught from those times to date
Meanwhile, how could it be otherwise, Euclides, dealt with the question of lines and in the Postulate number five of the aforementioned book of The Elements established the Parallel Postulate or also called the Fifth Postulate of Euclid. In it, it is stated that if a line, when it affects two other lines, makes the internal angles corresponding to the side less than two straight lines, the two lines prolonged indefinitely will be found on that side where the angles less than two straight lines are found.
