Parallel lines are those that do not intersect.
Parallel lines are those that will not intersect at any time . Its infinite sequences of points develop in such a way that there is no possibility of their intersecting in the plane .
For geometry , a line is an infinite succession of points that extends in the same direction. Straight lines, therefore, do not have a beginning or an end, unlike semi-lines (they have a beginning but no end) and segments (they begin and end at certain points). Parallel , on the other hand, is that which maintains equidistance with something and which, although it extends indefinitely, will never intersect with the other element, since both will not meet.
Parallel lines vs. secant lines
There are two possibilities that can involve the parallelism of two lines. One option is that both do not share any points ; the other, that the two are coincident (they share all the points). It should be noted that parallel lines have certain properties such as transitive (if a line a is parallel to b and b is parallel to c , a and c will also be parallel) and symmetry (if a is parallel to b , b is parallel a a ).
The case of secant lines is different, which share a single point. At this point, both lines intersect, which means that they do not maintain a parallel relationship. Intersecting lines are perpendicular when, when intersected, they form four right angles (90°).
To understand the concept of parallel lines, railroad tracks are usually taken as examples. The track's rails never intersect in their entire length. In theory , if these rails were extended to infinity, they would not intersect either.
Train tracks are straight parallel lines.
Parallelism in geometry
Parallelism is a relationship that belongs to the field of geometry and that can occur between all linear varieties whose dimension is equal to or greater than 1, a set that includes planes, hyperplanes and straight lines, among others. A linear variety, for its part, is the set that brings together all the solutions of a given system of linear equations (also called equations of the first degree , they are those that establish an equality and that only present additions or subtractions between one or higher variables. to the first power).
In other words, it is possible to say that there are more than one linear varieties that can present the parallelism relationship; Just as to graphically understand the idea of two parallel lines it is possible to resort to the image of a rail, in the case of planes one can think of two sheets of paper placed one on top of the other, although the planes are also infinite and therefore Therefore this representation is not entirely accurate.
Parallel lines in the Cartesian plane
Two lines are considered parallel if, when observed in the Cartesian plane, they have the same slope or are perpendicular to any of the axes; This occurs in the constant function . Let's look at each of the concepts just mentioned in detail:
- Cartesian plane : these are the Cartesian or rectangular coordinates; that is, those that are used to graphically represent a function and that have axes arranged orthogonally (orthogonality is, in this case, a synonym for "erpendicularity). By convention, when we think in two dimensions the axes are X and Y and Z is added for the three dimensions.
- Slope : is the degree of inclination that an element presents with respect to the horizontal axis.
- Constant function : it is the mathematical function that takes the same value for every value of the independent variable (the one that takes different values and that affects that of the dependent variable).