/ / Perpendicular lines and their properties

Perpendicular lines and their properties

Perpendicularity is the ratio betweenvarious objects in Euclidean space — straight lines, planes, vectors, subspaces, and so on. In this material, we take a closer look at the perpendicular lines and characteristics that are relevant to them. Two straight lines can be called perpendicular (or mutually perpendicular) if all four corners that are formed by their intersection are strictly ninety degrees.

perpendicular lines

There are certain properties of perpendicular lines implemented on the plane:

  • The lesser of those angles that are formed by the intersection of two straight lines in one plane is called the angle between the two straight 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 straight line perpendicular to the plane implies that the straight line will be perpendicular to all straight lines that lie on this plane.
  • Rays or segments lying on perpendicular lines will also be called perpendicular.
  • Perpendicular to any particular line will be called that line segment, which is perpendicular to it and has as one of its ends a point where the line and the segment intersect.
    perpendicular conditions of straight lines
  • From any point that does not lie on this straight line, it is possible to omit only one straight line, perpendicular to it.
  • The length of a perpendicular straight line, dropped from a point onto another straight line, will be called the distance from a straight line to a point.
  • The condition of perpendicularity of straight lines is that those can be called straight lines that intersect strictly at right angles.
  • The distance from any particular point of one of the straight parallel lines to the second straight line will be called the distance between two parallel straight lines.

Construction of perpendicular lines

Perpendicular lines are built on a plane withusing 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

equation of a straight perpendicular plane
drawing square with this straight line and draw a second straight along the second side of this right angle. This will create two perpendicular lines.

Three-dimensional space

An interesting fact is that the perpendicular linescan be implemented in three-dimensional spaces. In this case, two straight lines will be called such if they are parallel, respectively, to any two other straight lines lying in the same plane and also perpendicular to it. In addition, if on a plane only two straight lines can be perpendicular, then in three-dimensional space there are already three. Moreover, in multidimensional spaces, the number of perpendicular lines (or planes) can be further increased.