Mathematical+Reflections+p.58

Chaeyoung Lim 3/22/2011 Math 7B

Big Idea Many things in our world are mathematically similar and we can use this to understand and describe the world around us.

Essential Question # 4/5  What types situations can I use my similarity ideas to solve?

Mathematical Reflection 4 A. I can decide it by seeing the figures' general shape, corresponding side lengths (increased by the scale factor), and angle measures.
 * Q1. How can you decide whether two figures are similar?**

A2. When i multiply a scale factor, then the side lengths increased by times multiplied by the scale factor. And, the area is a number squared by a scale factor.
 * Q2. What does a scale factor between two similar figures tell you about the relationship between the length and area measures of a small figure.**

A3. I would first divide the percentage by 100 (e.g., 200%=200/100=2). I would then multiply this number with the length of the small figure, in order to obtatin the length of the large figure.
 * Q3. If the scale factor from a small figure to a large figure is given as a percent, how can you find the side lengths of a large figure from a small figure?**

A4a. They are not similar because even though they have same general shape and angle measure, the side lengths are not multiplied by the same scale factor →3/4≠8/9, 4/3≠9/8 b. Yes, they are similar. Scale factor from left to right is 1/3, and from right to left is 3.
 * Q4. Decide whether each pair of rectangles below is similar. If the rectangles are similar, give the scale factor from the rectangle on the left to the rectangle on the right. If they aren't, explain why**.

Summary In this investigation, I used scale factors and their relationship to find areas and side lengths in simlar figures to solve problems. I was able to detect the similar figures by seeing the three elements: general shape, angle measures, and side lengths (scale factor). To sum up my points, I learned how to detect similar figures, and how solve various situations using characteristics of the similar figures.