The Undefined Terms in Geometry

The 3 "undefined terms in geometry" are the building blocks for the rest of the subject.  They are like the big cinder blocks that are first placed at the bottom of a house - without those blocks, the rest of the house couldn't be built. 

The 3 terms are point, line, and plane.  Do not be intimidated by the the phrase "undefined."  You may already know a pretty good definition for these terms, especially the first two.

NEW!  For an exciting, interactive way to learn about the undefined terms in geometry, please take a look at our Geometer's Sketchpad Tutorial. (You will need windows media player to view the video) 


Defining the Undefined Terms in Geometry
Defining Undefined Terms
  • A point is like a star in the night sky.  It is a little spec in a large endless sky.  However, unlike starts, geometric points have no size.  Think of them as being so small that they take up zero amount of space.

  • A line is like the edge of a ruler, that never ends.  Take a ruler and draw a line - now imagine if that line kept going straight forever.  The line you have is thick enough for you to see, but you need to imagine that your line is so thin that you can't see it - it has no thickness at all.  That is a geometric line.

  • A plane is a flat piece of land (like a football field) that extends forever.  Imagine that you can pick that football field up, and put it anywhere in the air that you like.  You can even turn it side ways, or diagonally.  A plane is just a flat edge (like a piece of paper) that has no thickness (just like the line) and extends forever.


Connecting the Three Undefined Terms in Geometry

Take out a sheet of paper.  Draw a dot on that piece of paper - that will be our first point.  Next, draw another dot to represent point number two.  Once you have the two points drawn, take a ruler and draw a straight line through those points.  Make sure your line goes to the very edge of your piece of paper.  You should have something that looks like this...

Undefined TermsFrom here, you are going to have to use your imagination a little bit.  Pretend that your piece of paper goes on forever in all directions.  This piece of paper could cover the entire world.  You need to also pretend that the line you have drawn never stops either.  After you've done this...

  • The dots are geometric points
  • The line drawn through the points is a geometric line, and
  • The piece of paper is a plane. 
Labeling Undefined Terms

Points are named by capital letters.  Remember, points have no size, but we draw them as a "dot" on our papers so that we know where they are.  Any letter can be used to name a point.  Here we have points A, J, and X.

Line AB

Lines are named in two different ways.  You can choose whichever way you like better.  The first way giving it a lowercase letter.  In this case we have line t


Lines can also be named by two of the points that the line goes through.  Here we have a line passing through points A and B.  Notice how we drawn arrows at the end of the line?  This tells us that our line extends forever without having to draw it to the edgeLines of our paper every time.  To correctly label this line, write the letters AB with a line and arrows on top of it like the one shown at the right...

Just like lines, planes too can be named in two different ways.  Again, you can Plane Rchoose whichever way you like.  The first way is to name it with a capital scripted (cursive) letter.  In this case we have Plane R

Planes can also be named by naming any three points that are within the plane.  Again, our plane is the piece of paper (it goes on forever) and the points A, J, and X all are on that plane.  We could also name this:  Plane AJX.

We hope that you now have an understanding (if not a definition) of the three undefined terms in geometry.  These three terms will be used in many more vocabulary terms throughout your times studying geometry.  So if you don't understand them completely, come back and read this page again sometime.  You may also want to view the GSP tutorial shown at the top of the page - we highly recommend it.


Are you now able to "define" the undefined terms in geometry?! 

Want more free geometry help?  Return from the  the undefined terms in geometry to free geometry help page or visit the GradeA homepage for even more free math help resources.


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