Elements of Geometry
Point
Definition Point
A point shows an exact position in space. We draw a point as a small dot.
Definition Point Notation
We usually name a point with a capital letter, such as \(A\).
In mathematics, we imagine that a point has no size or shape. It only marks a position.
Example
The diagram below shows three points labeled \(A\), \(B\), and \(C\):
Lines, Segments and Rays
Definition Line
A line is a straight path that goes on forever in both directions.
Definition Line Notation
We name a line using any two points on it, written as \(\Line{AB}\). We read this as “line \(AB\)”.
Example
Name the line shown below:
The line is \(\Line{EF}\).
Definition Line Segment
A line segment is the part of a line between two endpoints. It has a fixed length.
Definition Line Segment Notation
We name a line segment by its endpoints, written as \(\Segment{AB}\). We read this as “segment \(AB\)”.
Example
Name the segment shown below:
The segment is \(\Segment{EF}\).
Definition Ray
A ray is a part of a line that starts at one endpoint and goes on forever in one direction.
Definition Ray Notation
We name a ray by its endpoint first and another point on it, written as \(\Ray{AB}\). We read this as “ray \(AB\)”.
Example
Name the ray shown below:
The ray is \(\Ray{EF}\).
Intersection Point
Definition Intersection Point
An intersection point is a point where two or more lines, segments, or rays cross each other.
Example
Find the intersection point of the lines \(\Line{AB}\) and \(\Line{CD}\).
The intersection point is \(I\).
Parallel Lines
Definition Parallel Lines
Two parallel lines are lines that are always the same distance apart and never meet, even if you extend them.
Definition Parallel Line Notation
On a diagram, parallel lines are shown using matching little arrows on each line.