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Similarity Transformation

Similarity Transformation. Standard: G. SRT.2. Definition : Similar polygons are polygons in which: The ratios of the measures of corresponding sides are equal. Corresponding angles are congruent. Similar figures : figures that have the same shape but not necessarily the same size.

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Similarity Transformation

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  1. Similarity Transformation Standard: G. SRT.2

  2. Definition: Similar polygons are polygons in which: • The ratios of the measures of corresponding sides are equal. • Corresponding angles are congruent.

  3. Similar figures: figures that have the same shape but not necessarily the same size. Dilation: when a figure is enlarged to be similar to another figure. Reduction: when a figure is made smaller it also produces similar figures.

  4. Proving shapes similar: • Similar shapes will have the corresponding sides are Proportional. • Similar shapes will have all pairs of corresponding angles congruent.

  5. Similarity Statement ∆ABC ~ ∆DEF D A 8 12 4 6 B C E F 5 10 Therefore: A corresponds to D, B corresponds to E, and C corresponds to F. • The measures of all pairs of corresponding sides are Proportional. = = =

  6. Each pair of corresponding angles are congruent. <B <E <A <D <C <F

  7. Similarity Statement ∆RST ~ ∆LMN 1. Write the measures of all pairs of corresponding sides . 2. Write measures of all pairs of corresponding angles.

  8. Given ∆BAT ~ ∆DOTOT = 15, BT = 12, TD = 9 Find the value of x(AO). A x AT = BTOT TD O 15 x + 15 = 12 15 9 D x = 5 B 12 9 T Hint: set up and use Means-Extremes Product Theorem.

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