The two simplest objects in geometry are points and lines.
A point is a coordinate that marks a position in space (on a number line, on a plane or in three dimensions or even more) and is denoted by a dot. Points are usually labelled with a capital letter. Some examples of how points can be represented are shown in Figure 1.
A line is a continuous set of coordinates in space and can be thought of as being formed when many points are placed next to each other. Lines can be straight or curved, but are always continuous. This means that there are never any breaks in the lines (if there are, they would be distinct lines denoted separately). The endpoints of lines are labeled with capital letters. Examples of two lines are shown in Figure 1.
Lines are labelled according to the start point and end point. We call the line that starts at a point AA and ends at a point BB, ABAB. Since the line from point BB to point AA is the same as the line from point AA to point BB, we have that AB=BAAB=BA.
When there is no ambiguity (which is the case throughout this text) the length of the line between points AA and BB is also denoted ABAB
, the same as the notation to refer to the line itself. So if we say
AB=CDAB=CD
we mean that the length of the line between
AA and
BB is equal to the length of the line between
CC and
DD.
Note: in higher mathematics, where there might be some ambiguity between when we want refer to the length of the line and when we just want to refer to the line itself, the notation ABAB
is usually used to refer to the length of the line. In this case, if one says
AB=CDAB=CD, it means the lengths of the lines are the same, whereas if one says
AB=CDAB=CD, it means that the two lines actually coincide (i.e. they are the same). Throughout this text, however, this notation will not be used, and
AB=CDAB=CD ALWAYS implies that the lengths are the same.
A line is measured in units of length. Some common units of length are listed in Table 1.
Table 1: Some common units of length and their abbreviations.
Unit of Length

Abbreviation

kilometre 
km 
metre 
m 
centimetre 
cm 
millimetre 
mm 