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Stretching and Shrinking Similarity Similarity Similar figures have the same shape but not necessarily the same size. MathScience Innovation Center © 2007 Tests for Similarity • The measures of their corresponding angles are equal. • The lengths of their corresponding sides increase by the same scale factor. MathScience Innovation Center © 2007 Question 1 - Review Each of the shapes below have five sides and 5 angles, but which shape is similar to Z? Z 1. Choice One 2. Choice Two A 3. Choice Three B ic e ho C C ho ic e Th Tw o O ic e ho C MathScience Innovation Center © 2007 0% re e 0% ne 0% Question 2- Review Triangle RST is an enlargement of triangle WXY. Which answer choice lists a pair of corresponding S sides? X 0% 0% 0% d an ST an ST an T R 0% d XW d d an S MathScience Innovation Center © 2007 Y YW W XY T R W Y RS and WY RT and XW ST and XY ST and YW R 1. 2. 3. 4. Question 3 - Review Triangle RST is an enlargement of triangle WXY. Which answer choice lists a pair of corresponding S angles? XWY Y T MathScience Innovation Center © 2007 0% d 0% an 0% d 0% d WYX an R an XWY XYW W d and and and and an 1. RST 2. RTS 3. STR 4. SRT X Question 4 - Review If two figures are similar, which of the following might be different? 0% 0% 0% 0% a. number of sides b. shape c. size of angles d. area MathScience Innovation Center © 2007 Activity 1 The first shape is a self-similar shape and the second is not. What do you think a self-similar shape is? MathScience Innovation Center © 2007 Question 1 – Activity 1 Is the number of copies of an original shape used to make a new shape related to the side lengths or the area of the new shape? 0% 0% 1. Side lengths 2. Area of new shape MathScience Innovation Center © 2007 Question 2 – Activity 1 Quad 1 Quad 2 Are these two quadrilaterals mathematically similar? 0% o Ye MathScience Innovation Center © 2007 s 0% N 1. Yes 2. No Question 3 – Activity 1 Can the larger shape be divided into smaller congruent shapes that are similar to the original? 0% o Ye MathScience Innovation Center © 2007 s 0% N 1. Yes 2. No YES MathScience Innovation Center © 2007 Question 1 – Activity 2 What can be said about the angles of similar figures 0% 0% 0% 1. The angles are different. 2. The angles are the same. 3. The angles change by 180°. MathScience Innovation Center © 2007 Question 2 – Activity 2 Does the concept of similarity apply to three dimensional shapes? 1. Yes 2. No o Ye MathScience Innovation Center © 2007 s Scale Models 0% N 0% Shrinking Cups What would happen if you were smaller? What challenges would you face if were much smaller, only inches tall? MathScience Innovation Center © 2007 Shrinking Cups What challenges would you face if you had to design a cup to drink from if you were only 6-12 inches tall? Would we have to consider any aspects other than size? MathScience Innovation Center © 2007