8.3 Similar Polygons

Identifying Similar Polygons

Similar polygons If ABCD ~ EFGH, then A B C D E F G H *Statement of Proportionality— a proportion extended to show the ratios of all corresponding sides. *

Similar polygons Given ABCD ~ EFGH, solve for x. A B C D E F GH x 2x = 24 x = 12

Is ABC ~ DEF? Explain. A B C D E F ?? yes no ABC is not similar to DEF since corresponding sides are not proportional.

Similar polygons Given ABCD ~ EFGH, solve for the variables. A B C D E F GH x 10 y

If two polygons are similar, then the ratio of the lengths of two corresponding sides is called the scale factor. Ex: Scale factor of this triangle is 1: /6 or 4.5/9 = 1/2

Quadrilateral JKLM is similar to PQRS. Find the value of z. J KL M P Q R S z 6 15z = 60 z = 4

Theorem If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths. If KLMN ~ PQRS, then Ratio of Perimeters Statement of Proportionality

Given ABC ~ DEF, find the scale factor of ABC to DEF and find the perimeter of each polygon. A B CD E F 4 x y CORRESPONDING SIDES 4 : 8 1 : 2 so x = 6 and y = 10! P = = 20 P = = 40 The perimeters of similar figures have the same ratio as the corresponding sides!!!