You have learned about the following topics:
writing ratios and using them to solve problems
identifying similar polygons
solving problems that involve a scale factor or a scale drawing
identifying similarity transformations
proving that two triangles are similar
using similarity to find unknown triangle measurements
finding and using relationships in similar right triangles
finding the geometric mean
Reflect on each of these topics and answer two of the following questions:
Which topic in this unit do you feel the most confident about and why?
Which topic in this unit has been the most challenging for you and why?
What is an example of similar triangles or polygons that you may see in the real world?
I feel the most confident about writing ratios and using them to solve problems. This topic was relatively straightforward for me because it involved applying basic mathematical concepts to solve problems. I found it easy to understand and apply the concept of ratios to different scenarios.
The most challenging topic for me was proving that two triangles are similar. This topic was more abstract and required me to use geometric proofs to demonstrate similarity. I struggled with the logical reasoning and steps involved in proving similarity, but with practice and guidance, I was able to improve my understanding.
An example of similar triangles in the real world is the similarity between buildings. If you look at a city skyline, you may notice that different buildings have similar shapes and proportions. This similarity allows architects and engineers to apply the same design and construction techniques to different buildings, saving time and resources. Additionally, medical imagery such as X-rays or MRIs often use similar triangles to determine the size and position of internal organs or structures in the human body.