Proportions in Similar Figures

You will need a ruler for this activity. Work on this activity with a partner.

In Chapter 9, you learned that the image of a figure under a size change of magnitude k is similar to the original figure. In this activity, you will learn how to determine the size change factor when given two similar figures. (use the Geometer's Sketchpad model to help you.)

1. Polygons ABCDE and A'B'C'D'E' below are similar. Measure the lengths of corresponding sides. Then compute AB over AB', BC over BC', CD over CD', DE over DE', and AE over AE'.
   
   
   
   
2. A'B'C'D'E' is the size change image of ABCDE under a size change of magnitude 3. How does this size change magnitude compare to the ratios of lengths of corresponding sides that you found?
   
   
3. Pick a size change magnitude to use to draw a picture of the house below that is similar to the original. Do not tell your partner the size change magnitude you chose. After you and your partner have both drawn the image of the house, trade pictures. Measure the lengths of segments on your partner’s drawing and compute appropriate ratios to try to find out what size change magnitude your partner used.
   
   
   
   
4. Draw conclusions. With your partner, determine what you can say about the ratios of lengths of corresponding sides of similar figures.