8 3 Similar Polygons Two polygons are similar

8. 3 – Similar Polygons Two polygons are similar if: -their corresponding angles are congruent -their corresponding sides are proportional ~ “similar to” R U I L P S A G

Angles are Congruent <A <P <I <L Sides are Proportional <G <S <R <U I P A PILA~SRUG R L U S G

Are the two triangles similar? If so, write the similarity statement. R I 5 3 P 4 30º 10 S G SIP~RGU 60º 6 8 U

Scale Factor – the common ratio of the corresponding sides of similar polygons R I 5 3 P 4 30º S Find the scale factor of PSI to URG ½ 10 G 60º 6 8 U

Are the two triangles similar? If so, what is the scale factor? 8 4 40º 5 Not similar! 12 50º 6 8

Given that PILA~SRUG, determine the values of a, b, x and y. a= 60º X=4 b = 20º Y=3 3 I bº 1 P 2 60º A x L R 9 y 20º 12 S 6 aº G U

ABC and ABD are both isosceles triangles with AB = AC and AD = BD. 1) Are the corresponding angles congruent? 2) Write a. Asimilarity statement. B 70° C D

Given that QP // ON, Prove that the triangles are similar. -Because QP // ON, there are 2 sets of corresponding angles. Q -The triangles share third angle at M, so corresponding angles are congruent 6 12 O 3 - Since are proportional! 4 M 70° 2 N 4 P , corresponding sides

The figures are both squares. Are they similar? 4 to 7 What is the scale factor? Find the perimeter of ABCD 8 What is the ratio of their perimeters? 8/14 = 4/7 Find the perimeter of EFGH 14 E A D 2 F B C H 7/2 G

So… Theorem 8. 1 – If two polygons are similar, then the ratio of their perimeters is equal to the ratio of their corresponding sides.