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Exercise

Exercise. Compare by using >, <, or =. 9 12. 11 16. >. Exercise. Compare by using >, <, or =. 12 18. 8 12. =. Exercise. Compare by using >, <, or =. 1628. 13 21. <. Exercise. Solve the proportion. x 15. 16 12. =. x = 20. 14 5. 4 5. d = = 2 = 2.8. Exercise.

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Exercise

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  1. Exercise Compare by using >, <, or =. 912 1116 >

  2. Exercise Compare by using >, <, or =. 1218 812 =

  3. Exercise Compare by using >, <, or =. 1628 1321 <

  4. Exercise Solve the proportion. x15 1612 = x = 20

  5. 145 45 d = = 2 = 2.8 Exercise Solve the proportion. 57 2d =

  6. Congruent Polygons • Congruent polygons are polygons with the same size and shape.

  7. C • F • A • B • D • E

  8. same place in different figures • corresponding angles • corresponding sides

  9. Congruent Angles • Congruent angles are angles with the same measure.

  10. Congruent Segments • Congruent segments are segments with the same length.

  11. congruence symbol

  12. AD • BE • CF • Corresponding Angles • Corresponding angles are congruent (have the same measure).

  13. C • F • A • B • D • E

  14. ACDF • ABDE • BCEF • Corresponding Sides • Corresponding sides are congruent (have the same length).

  15. X Example 1 RSTXYZ. Complete each statement. S Y R T Z X R

  16. Y Example 1 RSTXYZ. Complete each statement. S Y R T Z X S

  17. Z Example 1 RSTXYZ. Complete each statement. S Y R T Z X T

  18. XZ Example 1 RSTXYZ. Complete each statement. S Y R T Z X RT

  19. XY Example 1 RSTXYZ. Complete each statement. S Y R T Z X RS

  20. YZ Example 1 RSTXYZ. Complete each statement. S Y R T Z X ST

  21. Similar Polygons • Similar polygons are polygons that have the same shape but not necessarily the same size. The symbol ~ means “is similar to.”

  22. Theorem • If two polygons are similar, then the corresponding angles are congruent and the lengths of the corresponding sides are proportional.

  23. AD • BE • CF B • Corresponding Angles 9 6 12 A C E 6 4 D 8 F

  24. ABDE • ACDF • BCEF B • Corresponding Sides 9 6 12 A C E 6 4 D 8 F

  25. ABDE • 6 4 • 3 2 = = • ACDF • 12 8 • 3 2 = = • BCEF • 9 6 • 3 2 = =

  26. scale factor—ratio of corresponding dimensions in similar figures

  27. Example 2 RST ~ XYZ. Use a proportion to find XY. Y S 10 15 9 X 12 Z 18 R T

  28. XZRT • XYRS = • XY9 • 2 3 = • 3 • 3 • 3(XY) = 18 XY = 6

  29. FD • ABFE = Example ABC ~ FED. Complete the ratio. D C 8 6 A F B E AC

  30. Example ABC ~ FED. If BC = 9, what is ED? D C 8 6 A F B E 12

  31. Example ABC ~ FED. If the perimeter of ABC is 30, what is the perimeter of FED?

  32. D C 8 6 A F B E 40

  33. Example ABC ~ FED. If mA = 85° and m E = 30°, what is the mC? D C 8 6 A F B E 65°

  34. Example Are PQR and JKL similar? L Q 8 6 18 J 12 P 12 8 K no R

  35. Example What length of PQ would make them similar? L Q 8 6 18 J 12 P 12 8 K 9 R

  36. Example Assume the two parallelograms are similar. 12 B C F G 9 6 A D E FG = 8

  37. Example Assume the two parallelograms are similar. 12 B C F G 9 6 A D E AE = 4

  38. Example If the diagonal AC = 15, what is the length of EG? 12 B C F G 9 6 A D E 10

  39. Example What is the perimeter of EFGD? 12 B C F G 9 6 A D E 28

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