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. 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 corresponding sides are Proportional. Similar shapes will have all pairs of corresponding angles congruent.

∆ABC ~ ∆DEF Similarity Statement = = = 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. = = =

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

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

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