Describe the concept of area and volume in terms of efficiency. What is the most efficient shape and why? How can we measure efficiency? An area is 2-dimensional, a plain figure, and covers outer space. While volume is 3-dimensional, is a solid figure, and covers all of the inner capacity. Area and volume help us determine the size and capacity of a shape. When we figure out the area and volume, we can make different shapes efficient, and to full potential. The circle is the most efficient shape. You can fit any other shape into a circle, as the circle still has room. The circle maximizes area and volume space. Efficiency is usually measured as the ratio of useful output to total input.
Explain how we can prove two triangles are similar. Well we can do many things to prove how 2 triangles are similar. Triangles have to have two angles that are the same (AA), which is when angle A of both triangles are the same. Another point we can prove how two triangles can be similar is when the ratio of two sides and one at corresponding angles are equal. For example, we can get two triangles, one with three sides of lets say 3, 5, and 9. And another triangle with sides of 6, 15, and 36. You can either multiply the first triangle, 3x2, 5x3, and 9x4. This will show us how both of the triangles are similar but different sizes. We can also divide the same numbers for the second triangle, and get the same number of sides. Another way of showing and proving triangles are similar is if all of the ratios of the triangle are equal as well. This is all how you can prove triangles are similar.
Project Reflection How do you think you have grown in your understanding of geometry?
During my tessellation project, I had no idea what it was, how to do it, or why we were even doing it. I kind of just laid off the project for a few days if I'm going to be honest, until I asked for help with what we were doing. Ande described the project, and how we can make our own. It was very simple and I was honestly very excited to work on it. He gave us a video to watch so we can make our own designs within a hexagon shape. Once we watched the video, I created my own design for my tessellation. It looked like a rocket, and I added different lines around to connect into the hexagon so I would have more complicity with my design. This helped me understand the geometry of the project. We would create different shapes and lines to make patterns with a straightedge and compass. I struggled a little bit with how I was going to make my whole project on a poster board, but thankfully my friend Mae helped me understand and lay out the basics for my poster. I wrote out my hexagons on the poster, and stenciled on my design for the middle of the hexagons. After that, I added more lines and shapes inside so I would have a repeated pattern all throughout my poster. I felt really confident in my work and my understanding of geometry. I colored the patterns that matched together on my poster and I feel like it was great work, and I am very proud of how it came out.