Math Portfolio 1
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This units main goal was to use similar triangles to measure the length of a shadow. While using the variables D, H, and L, we have figured out a formula to measure a shadows length. In order to do this though, everyone had to learn the basic concepts of similarity, congruence, right triangles, and trigonometry.
Similarity and congruence were two very important factors because they helped us learn about angles and the importance of triangles. Similarity was a key to find out how to use proportions to figure out unknowns (such as in HW7). Once similarity was learned we moved on to congruence where we learned proof and how to show others what is truth by giving them accurate facts based on previous truths. If similar triangles share enough equal traits, they can be called congruent by ASA, SAS, SSS, and AAS.
Right triangles came next and with them we learned how and why they are special. As it turns out, right triangles are furtively hidden in many problems. Along with our unit problem to find out the length of a shadow. Trigonometry worked with right angles as we learned about tangent, sine and cosine. Using trigonometry, we could figure out unknowns that were considered unsolvable to us when we only knew about proportions.
All of these concepts and ideas really helped us find the final equation for finding the length of a shadow. They all built upon each other and with a little logical reasoning we were able to finally solve it. Using similarity, we were able to use proportions, which was the foundation of our shadows equation. With right triangles we knew how to position the proportions for them to make sense. And using logical reasoning we were able to set the proportion to solve for S (length of shadow).
One of the beginning assignments that never really seemed to fit in until the end was HW 4 N by N window. In this assignment, we had to create an equation to figure out how much wood would be used for a square window if the square panes inside were all 1×1 ft. This assignment was very important for us even though nobody ever really realized it because in the end we had to figure out an equation and this kind of served as a heads up for what was to come. I think it was a warm up in way because we had to figure out our own equation based on only a few facts to figure out a final unknown and that is what you have to do to set up proportions.
Homework 7 was based on using the measurement of the Statue of Libertys nose and my nose length to determine what would be the length of her leg. This problem was solved by making a proportion of her to nose to my nose and Ðx over the length of my leg. X being the Statue of Libertys leg. Or there was another proportion that would work just as well. Libertys nose over her leg (x) and my nose over my leg. After everyone solved this assignment, all of the answers were different because people have different noses and legs. This assignment taught us all how to set up proportions and solve for unknowns, of course this was something that we used a lot afterwards and used to solve for the final problems.
Homework 18 was about using similar triangles to figure how high different spiders were located. They could see each other through mirrors placed on the ground in between them. To solve this problem, you had to make similar right triangles by doing this:
This tied into figuring the unit problem because it used both similar triangles and proportions. Plus you had to come up with your own way of solving it. We did all of this in order to come up with our final equation.
Trigonometry was not exactly used to find the final equation, but you could probably apply it to the problem as well