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Chapter 11.6

Chapter 11.6. Exploring Similarity. Objectives. I will recognize similar figures I will use properties of similar figures to calculate missing sides. I will use proportional reasoning to determine congruence and similarity of triangles. Properties of Similar Polygons.

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Chapter 11.6

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  1. Chapter 11.6 Exploring Similarity

  2. Objectives • I will recognize similar figures • I will use properties of similar figures to calculate missing sides. • I will use proportional reasoning to determine congruence and similarity of triangles.

  3. Properties of Similar Polygons • 1. Corresponding angles have the same measure • 2. The ratios of corresponding side lengths are equal. • The symbol means “is similar to.”

  4. Examples of similar polygons • Two objects are similar if they have the same shape. They do not have to be the same size! Similar polygons NOT Similar polygons

  5. A C F D 5 3 B E Properties of Similarity • Given that write a statement describing the relationships among their angles and sides. Corresponding angles have the same measure. Ratios of corresponding side lengths are equal.

  6. A C F D 5 3 B E Scale Factor • The common ratio of one polygon to a similar polygon is called the scale factor. In the triangles below, BC = 3 and EF = 5 so the scale factor of

  7. U P 12 6 8 T Q R S 16 Using properties of similar figures • Given that , find the length of TU Step 1: Determine the corresponding sides Step 3: Cross multiply and Divide to solve for TU Step 2: Plug in the numbers given in the problem 8(TU) = 72 TU = 9

  8. U P 12 6 8 T Q R S 16 You try it!  • Given that , find the length of ST Step 1: Determine the corresponding sides Step 3: Cross multiply and Divide to solve for ST Step 2: Plug in the numbers given in the problem 8(ST) = 96 ST = 12

  9. Dilation • Enlarging or reducing a figure proportionally is called a dilation. The image after the dilation is similar to the original figure. Think of your eyes dilating!

  10. Drawing a dilation • A dilation enlarges or reduces a polygon by a scale factor to create a similar image. For example, Notice how every coordinate of the original triangle has been multiplied by the scale factor of 2

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