Perpendicularity refers to the relationship between various objects in Euclidean space - straight lines, planes, vectors, subspaces, and so on. In this material, we will take a closer look at the perpendicular straight and characteristic features related to them. Two straight lines can be called perpendicular (or mutually perpendicular) if all four angles that are formed by their intersection are strictly ninety degrees.
There are certain properties of perpendicular lines realized on the plane:
- The smaller of those angles that are formed by the intersection of two lines on the same plane is called the angle between two lines. In this paragraph, we are not talking about perpendicularity.
- Through a point that does not belong to a particular line, it is possible to draw only one line, which will be perpendicular to this line.
- The equation of a line perpendicular to the plane implies that the line will be perpendicular to all the lines that lie on this plane.
- Rays or segments lying on perpendicular lines will also be called perpendicular.
- The segment of a line that is perpendicular to it and has, as one of its ends, the point where the line and the segment intersect, will be called the perpendicular to any particular line.
- From any point that does not lie on a given line, it is possible to omit only one line perpendicular to it.
- The length of a perpendicular straight line dropped from a point to another line will be called the distance from the line to the point.
- The condition for the perpendicularity of the lines is that they can be called straight lines that intersect strictly at right angles.
- The distance from any particular point of one of the lines parallel to the second line will be called the distance between two parallel lines.
Building perpendicular straight lines
Perpendicular lines are built on a plane using a square. Any draftsman should keep in mind that an important feature of each square is that it necessarily has a right angle. To create two perpendicular lines, we need to combine one of the two sides of the right angle of our
drawing a square with a given straight line and draw a second straight line along the second side of this right angle. Thus, two perpendicular lines will be created.
Three-dimensional space
An interesting fact is that perpendicular lines can also be realized in three-dimensional spaces. In this case, two lines will be called such if they are parallel, respectively, to any two other lines lying in the same plane and also perpendicular to it. In addition, if only two lines can be perpendicular on the plane, then in three-dimensional space there are already three. Moreover, in multidimensional spaces the number of perpendicular lines (or planes) can be further increased.