EducationSecondary education and schools

Perpendicular lines and their properties

Perpendicularity is the relationship between various objects in Euclidean space - straight lines, planes, vectors, subspaces, and so on. In this material, we will look more closely 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.

There are certain properties of perpendicular straight lines realized on the plane:

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

Construction of perpendicular lines

Perpendicular straight lines are built on a plane using a square. Any draftsman should keep in mind that an important feature of each gon is that he 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 Of a drawing square with a given straight line and draw a second straight line along the second side of this right angle. In this way two perpendicular lines will be created.

Three-dimensional space

It is interesting that perpendicular lines can be realized 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 in it. In addition, if on the 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.

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