WARM UP Solve for x X + 1 = X X 1 You will have to use the Quadratic Formula!

8.2 Similarity 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. 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: Similar shapes will have the ratio of all corresponding sides equal. Similar shapes will have all pairs of corresponding angles congruent.

Example: ∆ABC ~ ∆DEF = = = 8 12 6 4 C E F B 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. = = =

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. (0,8) C E (0,4) N M D (0,0) (3,0) (6,0)

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

T61: 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.

<J comp. <K  <K = 50 <K = <M 50 = x + 5 45 = x H O <J comp. <K  <K = 50 <K = <M 50 = x + 5 45 = x

<H = <O 90 = y 180 = y

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