MR74

Marcello Kim 11-17-2008 block C day 30  **BI: Many things in our world are mathematically similar and we can use this to understand and describe the world around us.** = = = __//**MATHEMATICAL REFLECTION #5**//__ = 1. Question: **Explain at least two ways you can use similar triangles to measure things in the real world. Illustrate your ideas with an example.** Answer: First you can use the shadow method to get a height of an object. That's because at the same day, same time, the ratio of your height and the shadow is same. So you could use the method on the shadow of the object you want to measure at. Image: Also you can you mirrors which is a similar way like the shadow: 2. Question: **What properties of simmilar triangles are useful for estimating distances and heights?** Answer: As said in the question, the property of simmilarity is useful for measuring. Since simmliar figures have the same continous ratio for their corresponding sides, you could just get the ratio and use it at another corresponding side to get the measurement you need. Also, you can use other shapes too by using the steps above, but the triangle is the most efficient way. (I think) 3. Question: **If you take any 2 simmilar triangles and place the small one on top of the big one so that a pair of corresponding angles match, what can you say about the side of the two triangles opposite these corresponding angles?** Answer: They show a trapezoid and also they are parallel to each other. Also, you can use it for measuring objects by making the shorter opposite line the distance and use the divided triangles like above. But this time, the smaller triangle is inside the bigger one. It's used by getting the larger corresponding ratio this time. It's used in prob. 5.3. Image: Summary: In this investigation, I learned how to use simillar triangles to get measurements of differrent objects. Since the triangles are simillar, you can use corresponding side's ratios to determine what # you would multiply into the corresponding side needed to get the measurement. I also learned that the simillar triangles doesn't need to be apart to get distnaces. Like the overlapping triangles at prob. 5.3. Finally, I learned that at the same time, same place, shadows alway make a simllar triangle.
 * EQ 4/5 What types situations can I use my similarity ideas to solve? **