Tessellation Project
cover letter:
In this unit we focus on this question "What makes shapes efficient, and how is that demonstrated in nature" In this unit we study how to solve the area of the triangle. Then we find an equation to solve the area of a n-sided polygon. And we study how we can prove two triangles are similar. The step to solve n-sided regular polygons is to make a calculator in google sheet that can solve the area. To solve this we need to find the Theta, and the Theta means how many sides of this shape. Then we need to find the Side Length. We have 2 ways to solve what the Side Length is: one is Pythagorean Theorem: good when you know two sides, and no angles. The other one is SOH CAH TOA: good when you know an angle and a side. Lastly, we need to find an apothem, which is the height of the triangle. Then we can solve the area.
To prove how two triangles are similar is they all have the same angle no matter if the triangle is very big and one is very small as long as they have the same angle they are similar. The second way is that the ratio of corresponding sides are equal with the similar triangles. The third way is ratio of all sides are equal.
In this unit we focus on this question "What makes shapes efficient, and how is that demonstrated in nature" In this unit we study how to solve the area of the triangle. Then we find an equation to solve the area of a n-sided polygon. And we study how we can prove two triangles are similar. The step to solve n-sided regular polygons is to make a calculator in google sheet that can solve the area. To solve this we need to find the Theta, and the Theta means how many sides of this shape. Then we need to find the Side Length. We have 2 ways to solve what the Side Length is: one is Pythagorean Theorem: good when you know two sides, and no angles. The other one is SOH CAH TOA: good when you know an angle and a side. Lastly, we need to find an apothem, which is the height of the triangle. Then we can solve the area.
To prove how two triangles are similar is they all have the same angle no matter if the triangle is very big and one is very small as long as they have the same angle they are similar. The second way is that the ratio of corresponding sides are equal with the similar triangles. The third way is ratio of all sides are equal.
This is an example of side, angle, side (SAS). If you take side CB/AB you get 24/12=2, and then FE/FD you get 16/8=2. Since they both equal 2 the ratio of the sides are the same. Also both have 50 degree angles, so they both have the same angle. Since the ratio of the sides are the same, and they share the same angle this satisfies SAS, so the two triangles are similar.
Project reflection:
I think I have grown a lot with my understanding of geometry. In these units I have learned the sin, cos and tan. This is a way to solve the area of the triangle. And I know how to solve polygons. The challenges I have faced in these units is I have to draw a polygon on paper and on the computer just use a ruler and a compass and use those to finish my tessellation project. So in these units I think I have grown a lot in my understanding of geometry.
I think I have grown a lot with my understanding of geometry. In these units I have learned the sin, cos and tan. This is a way to solve the area of the triangle. And I know how to solve polygons. The challenges I have faced in these units is I have to draw a polygon on paper and on the computer just use a ruler and a compass and use those to finish my tessellation project. So in these units I think I have grown a lot in my understanding of geometry.