From Latin perpendicular, perpendicular is a term used in the geometry to name the flat or to line that, with another plane or line, creates a ninety degree angle. It is important to note that there are various forms of perpendicularity relationships.
Two lines that lie in the same plane are perpendicular when they form four right angles. In the case of rays, perpendicularity appears when right angles are developed, usually with the same point of origin. Finally, the planes and semi-planes are perpendicular in the cases in which four dihedral angles of ninety degrees are formed.
You may even develop a perpendicularity relationship between the elements mentioned above (straight, ray, plane, semi-plane), although considered 2 by 2.
Perpendicular vs. parallel
It is important to emphasize that when talking about perpendiculars we find another term that is related to them and that sometimes are often confused. We are referring to the so-called parallel ones.
In this case, we have to make it clear that parallel lines can be defined as those that never intersect, that are equidistant and that no matter how long they last, they never meet at a point.
However, in front of those are the perpendicular lines that, as we have previously analyzed in depth, are the ones that are characterized because they are the ones that intersect with others, forming what is a right angle. Therefore, we can establish that the difference between parallel and perpendicular is 90º.
In order to better understand this clear differentiation, nothing better than using two examples. Thus, the lines that make up a sign on the ground of a zebra crossing or those that delimit the width and length of a road are parallel straight lines. On the other hand, perpendiculars are the lines that give shape to the mathematical sign of the sum: +.
Properties of perpendicularity
Among the properties of perpendicularity are the uniqueness (Through a point belonging to a line, in a certain plane, only a perpendicular line passes) and the symmetry (When a figure is perpendicular to another, it will also be perpendicular to the first one). In the case that two lines intersect and create congruent adjacent angles, they are perpendicular, as are the planes that create perpendicular adjacent dihedral angles.
Another property of perpendicularity indicates that the sides of an angle and its opposite rays determine two perpendicular lines. In the same way, those sides that are part of a dihedral angle and their opposite half-planes also generate two perpendicular planes.
Other uses of the term perpendicular
It should be noted that it is known as bow perpendicular to the vertical line arising from the intersection of the maximum waterline with the applast edge of the stem of a vessel.
Finally, we have to underline the existence of a book that takes the concept that we are addressing as an integral part of its title. It is about the work “La perpendicular historia”, written by Carlos Fonseca Terán, in which a review is made of what the Sandinista revolution is while showing what the current reality of Nicaragua is.