8 3 Similar Polygons Warmup Simplify Identifying Similar

8. 3 Similar Polygons

Warmup - Simplify

Identifying Similar Polygons Definition: Similar Polygons n Two polygons such that their corresponding angles are congruent and the lengths of corresponding sides are proportional the two polygons.

Similar polygons n If ABCD ~ EFGH, C B A then G D F E H

Similar polygons n Given ABCD ~ EFGH, solve for x. C 6 G D x B F 2 4 A E 2 x = 24 x = 12 H

Is ABC ~ DEF? Explain. B 6 E 13 12 A D 5 10 C 7 F ABC is not similar to DEF since corresponding sides are not proportional. ? yes ? no

Similar polygons Given ABCD ~ EFGH, solve for the variables. G C H D 5 x B 2 A 10 F 6 E 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: 2 n 9 4. 5 3 6

n Quadrilateral JKLM is similar to PQRS. Find the value of z. R K L S Q 15 6 J 10 M 15 z = 60 z=4 z P

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

n Given ABC ~ DEF, find the scale factor of ABC to DEF and find the perimeter of each polygon. E P = 4 + 6 + 10 = 20 6 A P = 8 + 12 + 20 = 40 B 12 10 4 C D CORRESPONDING SIDES 4: 8 1: 2 20 8 F