# andand similarity shrinkingshrinking stretchingstretching

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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?

YesNoQuestion 2 Activity 1Quad 1Quad 2Are these two quadrilaterals mathematically similar?

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