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and and Similarity Similarity Shrinking Shrinking Stretching Stretching

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• andSimilarityShrinkingStretching

• SimilaritySimilar figures have the same shape but not necessarily the same size.

• Tests for SimilarityThe measures of their corresponding angles are equal.The lengths of their corresponding sides increase by the same scale factor.

• Each of the shapes below have five sides and 5 angles, but which shape is similar to Z?Choice OneChoice TwoChoice ThreeAB ZQuestion 1 - Review

• Triangle RST is an enlargement of triangle WXY. Which answer choice lists a pair of corresponding sides?

RS and WYRT and XWST and XYST and YWSRTWXYQuestion 2- Review

• Triangle RST is an enlargement of triangle WXY. Which answer choice lists a pair of corresponding angles?

and and and andQuestion 3 - Review

• Question 4 - Reviewa. number of sidesb. shapec. size of anglesd. areaIf two figures are similar, which of the following might be different?

• Activity 1 The first shape is a self-similar shape and the second is not. What do you think a self-similar shape is?

• Question 1 Activity 11. Side lengths2. Area of new shapeIs 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?

• Can the larger shape be divided into smaller congruent shapes that are similar to the original?

YesNoQuestion 3 Activity 1

• YES

• Question 1 Activity 21. The angles are different.2. The angles are the same.3. The angles change by 180.What can be said about the angles of similar figures

• Question 2 Activity 2YesNoDoes the concept of similarity apply to three dimensional shapes?Scale Models

• Shrinking CupsWhat would happen if you were smaller?

What challenges would you face if were much smaller, only inches tall?

• Shrinking CupsWhat 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?

Stretching and Shrinking http://MathInScience.info MathScience Innovation Center, 2007