Perpendicularity is the relationship between various objects in Euclidean space - lines, planes, vectors, subspaces, and so on. In this material, we will take a closer look at perpendicular lines and the characteristic features related to them. Two lines can be called perpendicular (or mutually perpendicular) if all four angles formed by their intersection are exactly ninety degrees.
There are certain properties of perpendicular lines implemented on a plane:
- The smallest of those angles formed by the intersection of two lines on the same plane is called the angle between the two lines. In this paragraph, we are not yet talking about perpendicularity.
- Through a point that does not belong to a particular line, it is possible to draw only one line that will be perpendicular to this line.
- The equation of a line perpendicular to a plane implies that the line will be perpendicular to all lines thatlie on this plane.
- Rays or segments lying on perpendicular lines will also be called perpendicular.
- Perpendicular to a particular line will be called that segment of the line that is perpendicular to it and has as one of its ends the point where the line and the segment intersect.
- From any point that does not lie on a given line, it is possible to drop only one line perpendicular to it.
- The length of a perpendicular line drawn from a point to another line will be called the distance from the line to the point.
- The condition of perpendicularity of lines is that they can be called lines that intersect strictly at right angles.
- The distance from any particular point of one of the parallel lines to the second line will be called the distance between two parallel lines.
Construction of perpendicular lines
Perpendicular lines are built on a plane using a square. Any draftsman should keep in mind that an important feature of every square is that it necessarily has a right angle. To create two perpendicular lines, we need to match one of the two sides of the right angle of our
drawing square with a given line and draw a second line along the second side of this right angle. This will create two perpendicular lines.
Three-dimensionalspace
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 straight lines can be perpendicular in a 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.
