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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.

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.

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.

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.

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*.

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.

Now move the compass to the bottom intersection and draw another medium-sized arc that intersects the one you just drew. Label this point of intersection of the two medium-sized arcs with a *D*. To finish, take your straight edge and connect points *B* and *D*.

This straight line is your angle bisector that cuts your angle in half exactly. You could do this method directly on your pie slice so you can see the line where you need to cut across to split your pie slice exactly in half. Just use a clean plastic tip instead of a pencil.

We've seen that this process is pretty neat. It uses no measuring or numbers. It uses a method called geometric construction, which is the drawing of lines, angles, and shapes with the use of only a pencil, compass, and straight edge. We've just learned how to use geometric construction to draw an **angle bisector**, the line that cuts an angle exactly in half. With this method, we can be sure that any angles we bisect are cut exactly in half. Using this method to cut a pie slice will ensure that everybody gets exactly the same amount.

After this lesson is done, you should know how to bisect an angle in half using only a compass and straight edge.

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Geometry: High School15 chapters | 160 lessons

- Line Segments & Rays: Definition & Measurement 3:59
- Types of Angles: Vertical, Corresponding, Alternate Interior & Others 10:28
- Geometric Constructions Using Lines and Angles 4:32
- Line Segment Bisection & Midpoint Theorem: Geometric Construction 4:39
- Dividing Line Segments into Equal Parts: Geometric Construction 5:22
- Parallel, Perpendicular and Transverse Lines 6:06
- Constructing Perpendicular Lines in Geometry 3:39
- Constructing an Angle Bisector in Geometry 3:36
- Practice Making Geometric Constructions with Tools 4:17
- Constructing Equilateral Triangles, Squares, and Regular Hexagons Inscribed in Circles 5:00
- Go to High School Geometry: Introduction to Geometric Figures

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