[scheduled:: 2025-01-20]

Constructing polygons

Concept summary and connections

https://artofproblemsolving.com/ebooks/intro-geometry-ebook/c9s5

FOR FUN: Weighing PI:

Can we measure a value for PI using a scale? Let's try it: use the laser to cut out 20 accurately-sized circles of paper. Weigh them and divide by 20. That will tell us how much paper it takes to make a circle of that diameter. Now, since we know that the area of a circle should be πr2, we can divide by r2. If we weight a ream of paper and divide by its total area, we can get a nice number for the the weight of a certain area of paper, so if we divide the current result by that, we should get..... PI!

Constructing these shapes is cool, but it gives you more than just the ability to make the shape. Remember that regular polygons have internal and external angles with known measures; that means that you can now construct angles with any of those measures! So, if you ever need a 108° angle, you just need to construct enough of a pentagon to get the first corner and edges defined, and you have exactly what you need.

You can also take half- and quarter- angles of all of these, which gives you even more options.

Worked examples

Follow the textbook examples and use GeoGebra geometry construction tools to construct:

Media resources

Guided practice

Homework