Dividing Line Segments into Equal Parts: Geometric Construction

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  • 0:05 Dividing Line Segments
  • 0:47 Number of Parts
  • 1:15 The Process
  • 4:21 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.

Watch this video lesson to learn one way to easily divide any line segment into as many equal parts as you need. Also, learn where in real life this skill comes in handy.

Dividing Line Segments

A divided line segment is probably something that you've seen in the real world without even realizing it. What is it, you ask? It's a straight line connecting two points that has been divided into a number of equal parts. If you've seen a railroad track, then you've seen a real-world example of a divided line segment. Pretend that you're looking at a railroad track for a moment. Do you see how the track is divided into equal parts by the bars that connect the two rails that the train rides on? When I say equal parts, I mean that the bars are evenly spaced.

In this video lesson, I will give you a fairly easy method you can use to divide any given line segment into any number of equal parts.

Number of Parts

This method will work if you are dividing the line segment, a line connecting two points, into two parts, three parts, or more. Usually, the problem will tell you how many equal parts it wants.

In the real world, designers and architects can choose the best number that will result in the most stable building. Just like with the railroad tracks, the bars are spaced the distance that they are to maximize the strength and stability of the tracks.

The Process

For the method that I am going to show you to divide line segments, you will need just two tools. The first tool you need is a straightedge, like the edge of a piece of cardboard. The second tool is a compass. You might want to grab a straightedge and compass so you can follow along. I am going to show you the process to divide a given line segment into 5 equal parts. You can use this process for any number of equal parts by changing the width in step 3.

1. Step one is to draw your line segment. Use your straightedge to draw your line segment. Mark your starting point as A and your end point as B. We will refer to these points as we continue. The letters label this particular line segment as line segment AB.

Line drawn in Step 1
line segment ab

2. Take your straightedge, and draw another line segment starting from point A and angle this line up and away from point B. You will end up with what looks like a giant angle symbol. While it doesn't matter how long this new line is, I would draw this line as long as or just a bit longer than the line segment AB.

Other line segment drawn in Step 2
second line drawn for example problem

3. Now take your compass, and set the width of the compass to roughly 1/5 the length of the new line. We are dividing by 5 because we want 5 equal parts. It doesn't have to be exact, so you can eyeball it. Use the width to divide the new line into 5 equal parts. Begin by placing the tip of your compass on point A and then drawing an arc across the new line with the free end. This creates an intersection between the arc you just drew and the new line. Then move the compass to the newly created intersection and draw another arc across the new line further up the line. Continue doing this until you have marked out five equal parts on the new line. Mark this last intersection as point C.

Line divided into 5 equal parts in Step 3
dividing line segments step 3

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