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...