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Similarity

Similarity. Lesson 8.2. 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

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  1. Similarity Lesson 8.2

  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 ratio of all corresponding sides equal. Similar shapes will have all pairs of corresponding angles congruent.

  5. Example: ∆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 ratios of the measures of all pairs of corresponding sides are equal. = = =

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

  7. ∆MCN is a dilation of ∆MED, with an enlargement ratio of 2:1 for each pair of corresponding sides. Find the lengths of the sides of ∆MCN. (0,8) C 8 MC = MN = CN = (0,4) E 6 10 D N M (0,0) (3,0) (6,0)

  8. Given: ABCD ~ EFGH, with measures shown. 1. Find FG, GH, and EH. FG = GH = EH = 6 B 6 F 9 4 A 4.5 A E C 7 3 D G 10.5 H PABCD = 20PEFGH = 30 = 2 3 2. Find the ratio of the perimeter of ABCD to the perimeter of EFGH.

  9. Theorem 61: The ratio of the perimeters of two similar polygons equals the ratio of any pair of corresponding sides.

  10. Given that ∆JHK ~ ∆POM, H = 90, J = 40, mM = x+5, and mO = y, find the values of x and y. First draw and identify corresponding angles. K M J P O H <J comp. <K  <K = 50 <K = <M 50 = x + 5 45 = x <H = <O 90 = y 180 = y

  11. 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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