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

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

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

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

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

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

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

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

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

So… Theorem 8.1 – If two polygons are similar, then the ratio of their perimeters is equal to the ratio of their corresponding sides.