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Geometry: High School15 chapters | 160 lessons

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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.

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.

The third undefined term is **plane**. Planes are not the flying kind we are familiar with but are flat surfaces that continue forever. You can think of them as an infinite amount of points connected together to form a flat surface that extends to infinity in all directions. Picture a flat sheet of paper that never ends and you have a plane. A plane goes to infinity in length and width but has no height. Even though the plane extends forever in all directions, on paper, planes are represented by quadrilaterals, four-sided figures. One capital letter is marked on the quadrilateral to label the plane. While points can be referred to by their letter alone, to refer to a plane, you include the word 'plane' along with the letter. So, a plane represented by a quadrilateral with the letter P on it is referred to as plane P.

The fourth undefined term is **set** which is a collection of things. Sets are used in geometry to group numbers or items together so they can be considered a unit in themselves. Sets are written with curly brackets surrounding the items in the group. For example, a set of numbers is written as {1, 3, 5} where the set consists of the numbers 1, 3, and 5.

So, what have we learned? We've learned that in geometry, there are four **undefined terms**. Undefined terms are those terms that don't require a formal definition. The four terms are point, line, plane, and set. A **point** is quite simply, a dot. Points are labeled with one capital letter. A **line** is an infinitely long straight mark or band. Lines are labeled with two capital letters that stand for two points on the line. A **plane** is a flat surface that extends forever in all directions. Planes are labeled with a capital letter along with the word 'plane.' A **set** is a collection of things. Sets are written with curly brackets surrounding the items in the set.

After watching this lesson, you should be able to identify and describe each of the four undefined terms of geometry.

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Geometry: High School15 chapters | 160 lessons

- What is Geometry? 4:36
- Inductive & Deductive Reasoning in Geometry: Definition & Uses 4:59
- Thales & Pythagoras: Early Contributions to Geometry 5:14
- The Axiomatic System: Definition & Properties 5:17
- Euclid's Axiomatic Geometry: Developments & Postulates 5:58
- Undefined Terms of Geometry: Concepts & Significance 5:23
- Algebraic Laws and Geometric Postulates 5:37
- Go to High School Geometry: Foundations of Geometry

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