Mathematical+Reflections+p.58+10-11+2011

TM Stretching and Shrinking Mathematical Reflection 4 21st March 2011 Math 7D

__ 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 __** - What types situations can I use my similarity ideas to solve?

1. ** How can you decide whether two figures are similar? ** You can decide whether two figures are similar by comparing their angle measures and side lengths to see if they are similar and you can say their similar if they share a common scale factor. Also you can tell if they are similar, visually by seeing if the two shapes have resemblance of each other. 

2. **What does the scale factor between two similar figures tell you about the relationships between the length and the area measures of the two figures?** The scale factor gives you the ratio as to how much the other similar shape increases/decreases by. This affects the lengths of both figures and the scale factor squared equals the area.

3. **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 the large figure from the side lengths of a small figure?** You convert the percentage into your scale factor. So for example if the small figure is increased by 100 % you need to find what that is as a scale factor. To find your scale factor out of a percentage you need to divide the percentage by 100. Which in this case would equal 1< so that’s your scale factor. Then you multiply the scale factor (1) by the original lengths which helps you get the new corresponding lengths to the shape.

4. **decide whether each pair of rectangles below are simalr. If the rectangles are similar, give the scale facto from the rectangle on the left to the rectangle to the right. If they are not explain why.** ** A. ** No the two figures aren’t similar. I know this because they don’t share a scale factor and I have tested that out for justification. ** B. ** Yes the two shapes are similar because they have a common scale factor which is 3 and all the angles are same measures (90 degrees).

__ Summary __ // In this investigation we worked with various problems and they all corresponded with the idea of similarities between shapes. Also a new kind of calculation was introduced to us. The fist problem in this investigation we had to find the measures of a figure from measuring an image. We also learned how to scale using percentages to make a figure bigger or smaller. //


 * 1) angle measure
 * 2) compare
 * 3) congruent
 * 4) corresponds/corresponding
 * 5) diameter
 * 6) image
 * 7) parallel
 * 8) perpendicular
 * 9) ratio
 * 10) scale
 * 11) scale factor
 * 12) similar
 * 13) vertex