andand Similarity ShrinkingShrinking StretchingStretching.

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Presentation transcript:

andand Similarity ShrinkingShrinking StretchingStretching

MathScience Innovation Center © 2007 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 Each of the shapes below have five sides and 5 angles, but which shape is similar to Z? 1.Choice One 2.Choice Two 3.Choice Three A B Z Question 1 - Review

MathScience Innovation Center © 2007 Triangle RST is an enlargement of triangle WXY. Which answer choice lists a pair of corresponding sides? 1.RS and WY 2.RT and XW 3.ST and XY 4.ST and YW S RT W X Y Question 2- Review

MathScience Innovation Center © 2007 Triangle RST is an enlargement of triangle WXY. Which answer choice lists a pair of corresponding angles? 1. and 2. and 3. and 4. and W X Y RT S Question 3 - Review

MathScience Innovation Center © 2007 Question 4 - Review If two figures are similar, which of the following might be different? 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? 1. Side lengths 2. Area of new shape

MathScience Innovation Center © Yes 2.No Question 2 – Activity 1 Quad 1Quad 2 Are these two quadrilaterals mathematically similar?

MathScience Innovation Center © 2007 Can the larger shape be divided into smaller congruent shapes that are similar to the original? 1.Yes 2.No Question 3 – Activity 1

MathScience Innovation Center © 2007 YES

MathScience Innovation Center © 2007 Question 1 – Activity 2 What can be said about the angles of similar figures 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 1.Yes 2.No Does the concept of similarity apply to three dimensional shapes? Scale Models

MathScience Innovation Center © 2007 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?