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8.3 – Similar Polygons

8.3 – Similar Polygons. R. U. I. L. Two polygons are similar if: -their corresponding angles are congruent -their corresponding sides are proportional ~ “similar to”. P. S. A. G. Angles are Congruent Sides are Proportional. R. U. I. L. <A <G <P <S <I <R

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8.3 – Similar Polygons

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  1. 8.3 – Similar Polygons R U I L Two polygons are similar if: -their corresponding angles are congruent -their corresponding sides are proportional ~ “similar to” P S A G

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

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

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

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

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

  7. 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

  8. 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

  9. 4 to 7 What is the scale factor? What is the ratio of their perimeters? Find the perimeter of ABCD 8 The figures are both squares. Are they similar? 8/14 = 4/7 Find the perimeter of EFGH 14 E F 2 B A D C H G 7/2

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

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