Constructing an Angle Bisector in Geometry

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  • 0:05 Angle Bisector
  • 0:37 Geometric Construction
  • 1:08 Setting Up
  • 1:45 The Process
  • 2:50 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 a cool way to split an angle in half. You can use this method to split a pie slice in half where you can be sure each side is equal.

Angle Bisector

In math terms, the line that splits an angle exactly in half is called the angle bisector. If you were looking at a pie slice, cutting on this line would split your pie slice exactly in half. You won't have to worry about your friend complaining that his or her slice is smaller than yours. If your friend does complain, you can use the method you are about to learn to show him or her that both pieces are indeed the same.

Geometric Construction

The method that I'm going to show you is pretty neat. It requires no measuring at all. Yes, that's right. You don't have to mess with any numbers for this lesson. This method is called geometric construction, which means the drawing of lines, angles, and shapes with only a pencil, compass, and straight edge. If you have these tools on hand, you will be able to cut a pie slice in half perfectly every time.

Setting Up

So go grab your tools if you have them. I want you to follow along so you can get a good feel for the process. To set up, what you need to do is to draw an angle. If you have a pie slice handy, you can simply outline the tip of the pie slice where the angle is for your angle. Once you have your angle, label the point where the angle is with B, the end of the top line with an A, and the end of the bottom line with a C. When you are done labeling, you will be looking at angle ABC.

Angle labelled ABC
ABC Angle

The Process

Take your compass and place it on point B. Set your compass width to approximately half of your bottom line. Now draw two small arcs intersecting both the bottom and top lines of your angle. Leaving your compass width the same, move the compass to the top intersection and draw a medium-sized arc somewhere in the middle of the opening of your angle.

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