5 examples of defined terms in geometry

Q: What are the 5 undefined terms in plane geometry?

Weve learned that in geometry, there are four undefined terms. Undefined terms are those terms that dont require a formal definition. The four terms are point, line, plane, and set. A point is quite simply, a dot.

Geometry is a very broad subject. What makes Geometry much different from algebra is that we aren't dealing with numerous mathematical operations. In Geometry, we are honing our reasoning and critical thinking skills. We are focused more on why something is the way it is rather than focusing on numerical calculations. That's not to say that we won't be performing any calculations in the subject, because we will be needing actual values, we'll need to use certain statements to solve problems and actually prove different scenarios. This is where our reasoning and critical thinking skills come in. Calculus relies heavily on these two skills. This won't be easy.

Table of Contents Show

What is an example of a defined term in geometry?
What are the 3 defined terms in geometry?
What are the 5 undefined terms in plane geometry?
What are examples of undefined terms in geometry?

Before we go too deep into the actual Geometry, we need to introduce some terms that we'll use in order to help solve problems and prove scenarios. Think of these terms as the building blocks of Geometry. Without these, we're stuck.

Undefined Term

An undefined term is a term that can't be defined so easily. There really isn't a definition to define such terms. Consider the word "the." We use the word "the" all of the time, but do we really know how to define the word "the?" "Am" is another word that can't be defined so easily. We can describe these terms, but we can't provide an actual definition. There are terms in Geometry that can't be defined so easily. We'll go over those later.

Defined Term

A defined term is, simply put, a term that has some sort of definition. Unlike "the" and "am", we can put a definition to the word "she." "She" just is defined as a term that represents us acknowledging that someone is female. Simple, right? In Geometry, we can use undefined terms to define a term.

Postulate

I like to call these statements the "well, duh" statements. These statements are "facts" that are accepted without proof. We can't approach proving these statements using conventional means. These statements are so basic that we can't use true technical jargon to explain them. However, if we use a little bit of critical thinking, we can use undefined and defined terms to help support a postulate.

Theorem

A theorem is completely opposite of a postulate. Theorems can be proven. We'll use different undefined and defined terms, as well as postulates to prove a certain statement. If a statement can be proven, then we have a theorem.

There is another term called a corollary, which is just a supplement to a theorem, but we'll get into corollaries later.

Those are the terms we'll be using throughout the subject. There's a lot of them, and they will likely some at you all at once. Focus and understand each statement.

Let's start with a few undefined and defined terms.

Simple Undefined Terms:

Point: A point just represents someone's position. That's all a point is. Where are you at? That's a point.

Line: A line is just a set of points that extends to one direction. It also works backwards. If we have points going due left, then we can also have points that go the opposite direction, straight right. Lines are indefinite, by the way. Later in the section, titles "Initial Postulates and Theorems You Should Know", we'll introduce a very important theorem that involve points and theorems.

Plane: A plane is the same as a line, except you have points everywhere, and the points don't go in one specific direction. It's a whole field of points.

Simple Defined Terms:

Line Segment: A line segment is just part of a line. Remember above when I said that lines are indefinite, and that they keep going and going? Line segments stop somewhere in both directions.

Ray: A ray is like a line, but the line takes off in one direction to infinity while the other side is like a line segment. The end of the line is called the endpoint.

Opposite Rays: Two rays that share the same endpoint that take off in opposite directions. The rays would create a line.

Angle: Two rays that share the same endpoint, however, the rays take off in different directions. The area in the middle of the two rays is the angle measure.

Ready to test your knowledge? Try a Problem Set.

Problem Sets

1. Give an example of an undefined term. What makes this term hard to define?

2. Give an example of a defined term. Give a definition of that term.

3. Give an example of a postulate. What makes your postulate hard to prove?

4. Give an example of a theorem. How did you prove your theorem?

5. Draw a point.

6. Draw a line.

7. Draw a line segment.

8. Draw a ray.

9. Draw a set of opposite rays.

10. Draw an angle.

What is an example of a defined term in geometry?

For example, an angle is a defined term in geometry, because we can define it as the corners that are produced when two lines intersect. That is, we can define an angle using other geometrical terms (in this definition, those terms are a line and an intersection point).

What are the 3 defined terms in geometry?

In Geometry, we define a point as a location and no size. A line is defined as something that extends infinitely in either direction but has no width and is one dimensional while a plane extends infinitely in two dimensions. There are three undefined terms in geometry.

What are the 5 undefined terms in plane geometry?

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.