# Pentagon Analysis (Final9)

- Author:
- A. Hurlburt

- Topic:
- Geometry

Over the course of spring 2021 I took Geometrical Reasoning. My favorite project over the course of the semester was creating shapes using the point tool, the segment tool, and the circle with center and radius tool. This brought together thinking that was developed with in the first week of class. This project allowed me to draw on my previous knowledge and successfully make a pentagon.
In this project the goal was to create a pentagon with sides equal to one and have all the angles equal to 108 degrees. To do this first we added a point anywhere (Point A). Next, we used the circle with center and radius to create a circle with radius one around point A. Then a point B was placed. It wasn't possible to know where to put the next point as we needed the angle to be equal to 108 degrees. This is where a "magic number" came in handy. This is also known as the law of cosine ---> sqrt (a^2+b^2-2*a*b*cos(C)=c^2. In this case a=1 b=1 and C=108 degrees. Now our magic number will help create the puzzle. The point that was most recently placed needs to have a circle with center and radius. Next, the point before the current point needs a center with circle and radius of the magic number. (example: C=circle with center and radius---> 1 and B= circle center and radius --> magic number). The two circles will create an intersection. Place a point where the circles meet. Now make a line segment. This line should be equal to one. Now, you can measure the angle (it will be 108 degrees). Lastly hide the circle. Repeat these steps until you have 5 sides (a pentagon).
The main reason I enjoyed this project was the fact that I was finally able to make sense of our first ever assignment in this class. I now had the knowledge to create shapes with equal side lengths that corresponded with the correct angles. This project was fun to create as one could watch the shape come together. This is a lesson that I would love to incorporate to my classroom in the future.
P.S Greg-- You were an amazing teacher

In this pentagon geogebra file, the law of ________ was used to create the magic number?

Does this law apply to hexagons and nonagons?

What is the formula for this law?

What is one aspect you still want to learn about when it comes to this process?