Undefined Terms of Geometry: Concepts & Significance

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  • 0:05 Undefined Terms
  • 1:12 Point
  • 1:52 Line
  • 2:57 Plane
  • 3:59 Set
  • 4:26 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

What do points, lines, planes, and sets have in common? Watch this video lesson to find out what they are, what they look like, and why they are called undefined terms.

Undefined Terms

How can something be undefined, especially in math? Surprisingly, there are four things that are undefined in geometry. This is what we will be talking about in this video lesson. We are not talking undefined in the sense that we would expect, but undefined in a different sense. These four things are called undefined terms because in geometry these are words that don't require a formal definition. They form the building blocks for formally defining or proving other words and theorems. These words themselves are considered so basic that they are considered to be true without having to be proved or formally defined.

So what are these four things? They are point, line, plane, and set. The first three are the more commonly referred to, but set is also one of them. Let's go on to see what each looks like and what each is.


Picture a dot, any dot, and you are looking at a point. Points are used a lot in geometry. They appear by themselves at times but most often you will see points in connection with various shapes. When you see them with shapes, they are usually located at the corners of these shapes. Points are labeled with capital letters. These points for example, can be labeled as points A, B, and C. Mathematically, points have no size, width, or height. They don't take up any space. They are simply used as position markers.


The next one on the list of undefined terms is line. A line is an infinitely long straight mark or band. We can also describe it as an infinite amount of points connected together. Lines go on forever in both directions but have no width or height. Picture anything straight, such as the edge of a ruler or the edge of a piece of paper, and you are looking at part of a line. If you extended your ruler's edge infinitely in both directions, you would have a line. Lines are labeled using any two points on the line or with one lowercase letter for the whole line. In geometry, lines have a special symbol made just for them. It looks like part of a line with arrows on both ends and we write it above two letters that stand for two points on the line. So line ST can be written using the symbol above both letters and on paper you would see the line going through both points S and T.

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