Mathematical+Reflections+p.74

Sunday, March 20th, 2011 Block 7H- Math  Ariyana Chowdhury

=Big Idea: Many things in the world are mathematically similar and we can use this to understand and describe the world around us. = =Essential Question: In what types of situations do I need to use my similarity ideas so that I can solve them? =

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==1. Explain at lest two ways you can use similar triangles to measure things in the real world. Illustrate your ideas with an example. ==

==One way you can use similar triangles measure things in the real world is by using shadows. This is done by by measuring the shadow of a meter stick, and then measuring the the shadow of whatever you're trying to find the height of. Afterwards you divide the shadow of the object by the shadow of the meter stick. You do this in order to get the scale factor. Next you multiply the shadow of the object by the scale factor. The answer you get to this is the height of whatever you were measuring. ==

*Even thought the picture says Broomstick's height we used a meter stick for this Investigation.

==**Another method for using similar triangles to measure real life objects is the mirror method, this method can be used indoors and is used outside when there aren't any shadows. You place the mirror on a flat, un-moving surface. This surface should be a good distance away from the object you are trying to measure. Then you need to back up until you can see the top of the object in the center of the mirror. Then you measure the distance between yourself and the center of the mirror. Afterwards you measure the distance from the center of the mirror to the object. You you divide the distance from the object to the center of the mirror by the distance from the center of the mirror to you. The sum of this is the scale factor. Then you multiply your height by the scale factor in order to get an accurate measurement of whatever itis you are trying to measure. ** ==

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==**2. What properties of similar triangles are useful for estimating distances and heights? ** == ==<span style="font-size: 1.3em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="font-family: 'Comic Sans MS',cursive; font-size: 13px; font-weight: normal; line-height: 19px;">One of the properties that make similar triangles useful for measuring heights and distances is that they have the same ratio between the side lengths, which makes it very east to find the scale factor between them. And when you have a scale factor then finding missing measurements is so much easier because you don not have to do a lot of work. Also side lengths are important in similar triangles because it doesn't matter wether of not you know the side lengths because you know they are similar. So you can just measure them and and then you can find an appropriate scale factor which will help find accurate measurements for objects. ** ==

==<span style="font-family: 'Comic Sans MS',cursive; font-size: 1.3em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;"> 3. If you take any two similar triangles and place the small triangle on top of the large triangle so that a pair of corresponding angles match, what can you say about the sides of the two triangles opposite these to corresponding angles? == ==<span style="font-family: 'Comic Sans MS',cursive; font-size: 13px; font-weight: normal; line-height: 18px;">The sides opposite the angles of the two similar triangles would be parallel with each other because first of all they never meet and second of all because they would be similar due to the fact that the triangles are similar which means the all the lines and angles are similar. They would also be parallel because they would be slanted at the same degree. ==



<span style="font-family: 'Comic Sans MS',cursive; font-size: 13px; font-weight: normal; line-height: 18px;">I learned a lot in Investigation 5. I learned that similar triangles are a huge help when it comes to measuring objects. I also learnt different methods of measuring tall structures such as the shadow method and the mirror method. I also perfected on how to find the missing lengths of objects using proportions and I brushed up on my ideas about parallel lines and similar triangles and I learnt a lot more about them because they were they main focus of this Investigation. I learned a lot because I didn't know about these methods of using similar triangles in order to measure large objects without having to physically measure them, but instead to use quick and easy mathematical procedures.



<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">Khan Academy- Video on Similar Triangles <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">Wolfram Alpha Mathematics- How Tall is that Building? <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">Silly Education Video- How Tall? <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">Your Teacher- Similar Triangles <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">The Adventures of Ernie and Stu- Similar Triangles Rap <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">GCSE Guide on Similar Triangles <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">Online Math Learning- Similar Triangles <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">Math Teacher- Similar Triangles