Points, Lines, and Planes
Points, lines and planes are the most basic elements of geometry.
To successfully solve geometry problems, it’s important to understand the purpose of these critical building blocks, how to read their diagrams, and how to name them properly.
Points, lines and planes will be important throughout the course, so dig in and learn everything you can about them!
Geometry has its own language, so make sure you understand these very important vocabulary words before you move on to the next lesson.
Vocabulary:
- point
- line
- plane
- collinear
- coplanar
- inersection
- space
- line segment
- ray
Point
A point is the simplest geometric figure.
It is represented by a dot on the page.
.
• A point indicates a location in space represented by a dot.
• A point has a location, but no size or shape.
• Points are named with a capital letter.
• On a graph, the position of a point is named by an ordered pair, (x,y).
Practice Locating Points with Geobra
Line
A line is a set of many points that extend without ending in opposite directions. A line can be named using any two points on the line, or with a single lowercase letter. The line shown here can be named FE, EF or m. We place a line with arrows on both ends over the two capital letters to indicate that we are defining a line.
Lines and Points
We combine lines and points to describe geometric figures. Since all lines in geometry are straight, points on a line are called collinear. On the line shown here, points P, T, and B are collinear. Points P, T, and L are not collinear. In geometry, these are called non-collinear points.
Line Segments
When you draw a line between any two points, you create a line segment. A line segment is part of a line.
We name a line segment with two endpoints.
This line segment can be named AB or BA.
Unlike a line, line segments have a beginning and an end, and therefore can be measured.
Name the line segment
Ray
A ray extends endlessly in one direction
Unlike a regular line that extends endlessly in both directions, a ray has a defined starting point, like the light from a flashlight.
A ray is named using the second letter on the side extending to infinity. This indicates direction.
Ray NP or 
The Plane Truth
A plane is a flat surface that extends in all directions endlessly and has no thickness.
It is a two dimensional surface with only length and width, but no height (or depth).
To name a plane, you can use any three points on the plane, as long as they are not collinear.
For example, we can name this plane ABC or CAB.
We cannot name it CBD because these points are on a line and therefore collinear.
Points A, B, C, D are coplanar.
But points C, D, I are not coplanar thus noncoplanar.
Undefined Terms
The three undefined terms in geometry are POINT, LINE, and PLANE!
Although it is hard to explain these terms, we can give examples of each.
Line
.
Plane
Point
Intersection
Two lines intersect at a point.
Two planes intersect at a line.
Space
In geometry, a plane is a simple flat surface.
On the other hand, space is a boundless, three-dimensional set of all points.
Space contains points, lines and planes.
Ready to Try It?
You are now ready test your knowledge of the geometric elements we explored here.
Practice Identifying Line Segments, Rays, and Lines with Geogebra
