Methods & Tools for Making Geometric Constructions

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  • 0:00 Geometric Constructions
  • 0:26 The Tools
  • 1:06 The Methods
  • 1:28 Bisecting a Line Segment
  • 1:58 Bisecting an Angle
  • 2:47 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.

Did you know that it's possible to do math without using numbers? This is exactly what Euclid did when he showed how to solve mathematical problems by drawing them out instead of with numbers.

Geometric Constructions

When you draw something accurately without the use of numbers, it is called geometric construction. Euclid showed us how these geometric constructions can be used to solve mathematical problems when you don't have numbers at your disposal. With just two tools you can bisect lines and angles as well as draw circumscribed and inscribed circles.

The Tools

So what are the two tools that you need? The two tools are your compass and your straightedge. If you count the pencil as a tool, then you have three tools. Note that I said straightedge and not a ruler. This is because a ruler has numbers. In true geometric construction, you don't have any numbers to deal with. The compass I mentioned isn't the one that has a needle that always point to the North Pole, but rather the type that you use to draw circles with. This type of compass has one end with a sharp point and a pencil point on the other. To use this tool, you put the pointy end down and you draw your arc with the other end by rotating the compass.

The Methods

You will be using the compass a lot to find important points. To do this, you normally place your compass at two different points and draw an arc from each point. These two arcs will intersect at your important point. You will repeat these steps to find more important points. The straightedge is then used to connect two or more of these important points. Let's take a look.

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