Similarity Lesson 8.2

Definition: Similar polygons are polygons in which: 1.The ratios of the measures of corresponding sides are equal. 2.Corresponding angles are congruent.

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.

Proving shapes similar: 1.Similar shapes will have the ratio of all corresponding sides equal. 2.Similar shapes will have all pairs of corresponding angles congruent.

Example: A CB D EF ∆ABC ~ ∆DEF Therefore: A corresponds to D, B corresponds to E, and C corresponds to F. 1.The ratios of the measures of all pairs of corresponding sides are equal. = = =

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

∆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. C N D M E (6,0) (3,0) ( 0,0) (0,4) (0,8) MC = MN = CN =

Given: ABCD ~ EFGH, with measures shown. 1. Find FG, GH, and EH. A A B D C G F E H Find the ratio of the perimeter of ABCD to the perimeter of EFGH. FG = GH = EH = P ABCD = 20 P EFGH = 30 = 2 3

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

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 H J M O P <J comp. <K  <K = 50 <K = <M 50 = x = x <H = <O 90 = y 180 = y

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