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Elementary Geometry – Open Lines

In this post, we are going to discover what an open line is and how it is different from a closed line. We will also see different types of open lines.

Before we begin, take a look at this post about straight and curved lines to refresh your memory.

Open Lines

We know that a line is open because its endpoints do not connect.

In this picture, you can see that the line begins at one point and ends at another. Since they do not connect, we know that it is open.

Closed Lines

On the other hand, we can draw closed lines without lifting our pencil off the paper, starting and ending at the same point.

The answer is closed. Try and see if you can draw the shape without lifting your pencil off the page, starting and ending at the same point!

Types of Open Lines

They are classified according to their shapes. Let’s learn about some types of open lines and how to classify them:

Straight Open Line

It is a series of points that are lined up one after another, all in the same direction. It is also the shortest path between two points.

open lines

Curved Open Line

The points on the line are always changing direction.

open lines

Polygonal Open Line

It consists of more than one open straight line with points going in different directions. These lines have the following shape:

open lines

Mixed Open Line

It is a mixture of open curved and open straight lines.

open lines

Activity with Open Lines

Now that we know what an open line is, let’s test our knowledge! In this section, we will look at an activity from a Smartick tutorial to check what we’ve just learned.

Classify the Following Lines

open lines


I hope that you have had fun learning with us. If you would like to keep learning and practicing, log in to Smartick and try our method for free!


Image 1: straight open

Image 2: polygonal open

Image 3: polygonal closed

Image 4: curved open

Image 5: curved closed

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Diane Ackerman
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