Designation of points and lines

 

Point and line are the main geometric figures.

 

Points are designated by uppercase Latin letters: А, В, С, …

Lines are designated by lowercase Latin letters a, b, c …

If point A lies on line a then it is written as А ∈ a (the sign ∈ designates belonging),

If point A does not lie on line a, then it is written as А ∉ a.

Properties of lines and points

a is a line. The point A does not lie on line a (А ∉ a). The point B lies on line a (В ∈ a)

Properties of lines and points. The main properties of points and lines on a plane are as follows:

In this section, we will consider the properties of lines, which do not coincide, i.e. do no lie on each other.

  • A line is infinite.
  • Whatever the line, there are points belonging to the line and points not belonging to it.
  • Through any two points it is possible to draw one line only.
  • If two lines have a common point, then these lines intersect.
  • Two lines cannot have two or more points.
  • Only one line can pass through any two points.

Consider Figure 1:

Point B belongs to line b as it lies on this line.

Point A belongs to line a as it lies on this line.

Point D does not belong to either line a or line b.

Lines а and b have the common point С, hence these lines intersect (at point С). Apart from point C, lines а and b do not have any other common points

Through any two points A and C it is possible to draw only one line a.

Properties of lines and points

Figure 1. Arrangement of points and lines on a plane

Main property of the arrangement of points on a line

 

Out of three points on a line, one and only one point lies between the other two.

Main property of the arrangement of points on a line

Three points А, В and С lie on line а. Out of these points only one can lie between the other two. Point C lies between points A and B.

Main property of the arrangement of points on a line