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CHAPTER 8: Sections By: THE A SQUAD (Annie and Andrew)

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Vocabulary Terms Dilation: A transformation that is not rigid and preserves the shape of an object despite size changes. Scale Factor: The number that both X and Y are multiplied by to get the Image. Similar Figures: Figures are similar when the image of the other is congruent by a dilation.

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Postulates and Theorems Polygon Similarity Postulate: Two polygons are similar if and only if there is a way of setting up a correspondence between their sides and angles such that each pair of corresponding angles is congruent and each pair of corresponding sides is proportional. Angle-Angle Postulate: If two angles are congruent to two angles of another triangle, then the triangles are similar. Side-Side-Side Theorem: If three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar. Side-Angle-Side Theorem: If two sides and their included angle are proportional/congruent respectively, then the triangles are similar.

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Examples: A CB D FE Given: AB= 8; BC= 3; AC= 14; DE= 4; EF= 1.5; DF= 7 Prove: Triangle ABC ~ Triangle DEF AB/DE= 8/4= 2BC/EF= 3/1.5= 2 AC/DF= 14/7= 2 Thus, the sides of the triangles are proportion and, by the SSS Similarity Theorem, Triangle ABC ~ Triangle DEF.

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More Examples: 23.6 y x z f g h Given:

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Daily Application

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Quiz: 1.Find the image of (3,3) for a dilation with scale factor 1/3. 2.Write a similarity statement for the two triangles. B CA F E D (1,1) ABC ~ FED ACB ~ FDE BAC ~ EFD BCA ~ EDF CBA ~ DEF CAB ~ DFE

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Quiz Continued 3. Find x and y for these similar rectangles. 18 xy /18 = 4/x6x = 72 x =12y = 12

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For more information… similar/triangles/index.htmlhttp://www.mathwarehouse.com/geometry/ similar/triangles/index.html

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