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8.3 Similar Polygons

8.3 Similar Polygons. Two polygons are similar if:. Their corresponding angles are congruent. Their corresponding sides are proportional. *The symbol ~ is used for similarity. . Ex. 1: JKLMN ~ STUVW. List the congruent angles. J  S K  T L  U  M  V N  W.

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8.3 Similar Polygons

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  1. 8.3 Similar Polygons

  2. Two polygons are similar if: • Their corresponding angles are congruent. • Their corresponding sides are proportional. *The symbol ~ is used for similarity.

  3. Ex. 1: JKLMN ~ STUVW List the congruent angles. J  SK  TL  U M  VN  W Write a proportionality statement. JK KL LM MN NJ = = = = ST TU UV VW WS

  4. Ex. 2: • Decide whether the figures are similar. If they are similar, write a similarity statement.

  5. SOLUTION: As shown, the corresponding angles of WXYZ and PQRS are congruent. We need to find out if the sides are proportional. WX 15 3 = = PQ 10 2 YZ 9 3 XY 6 3 = = = = RS 6 2 QR 4 2 WZ 12 3 = = PS 8 2 So, the two figures are similar. Similarity Statement: WXYZ ~ PQRS

  6. Ex. 3: Note: 4/3 is called the scale factor.

  7. Ex. 4: The ratios are not all the same. Therefore, the triangles are NOT similar.

  8. Ex. 5: Are these two polygons similar? No, the corresponding angles are not all congruent.

  9. Ex 6:

  10. Perimeter of ABCD 8 + 11 + 16 + 11 = 46 Perimeter of GHIJ 5.5 + 8 + 5.5 + 4 = 23 46 23 = 2 1

  11. Ex. 7:

  12. Ex. 8: • JKLM ~ PQRS.Find the value of z. PQ QR = JK KL z 6 = 10 15 15z = 60 z = 4

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