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6.4 – Prove Triangles Similar by AA

6.4 – Prove Triangles Similar by AA . AA Similarity (AA ~). Two triangles are similar if two of their corresponding angles are congruent. Use the diagram to complete the statement.  GHI. Use the diagram to complete the statement. GI. HI. GH.

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6.4 – Prove Triangles Similar by AA

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  1. 6.4 – Prove Triangles Similar by AA

  2. AA Similarity (AA ~) Two triangles are similar if two of their corresponding angles are congruent.

  3. Use the diagram to complete the statement. GHI

  4. Use the diagram to complete the statement. GI HI GH

  5. Use the diagram to complete the statement. x

  6. Use the diagram to complete the statement. 8

  7. Use the diagram to complete the statement. x 12x = 160 40 3 x =

  8. Use the diagram to complete the statement. 8 12y = 128 32 3 x =

  9. Use the diagram to complete the statement. DEF

  10. Use the diagram to complete the statement. BC DE FD

  11. Use the diagram to complete the statement. E

  12. Use the diagram to complete the statement. x y

  13. Use the diagram to complete the statement. x 16

  14. Use the diagram to complete the statement. x 16x = 72 x = 4.5

  15. Use the diagram to complete the statement. 6y = 128 64 3 x =

  16. Determine whether the triangles are similar. If they are, explain why andwrite a similarity statement. 47° No 26°

  17. Determine whether the triangles are similar. If they are, explain why andwrite a similarity statement. ABC  CDE ACB  ECD Yes, AA~ ABC ~ EDC

  18. Determine whether the triangles are similar. If they are, explain why andwrite a similarity statement. B  E 77° C  F 55° Yes, AA~ ABC ~ DEF

  19. Determine whether the triangles are similar. If they are, explain why andwrite a similarity statement. No 82° 72°

  20. Determine whether the triangles are similar. If they are, explain why andwrite a similarity statement. U  SVR T  VSR Yes, AA~ SRV ~ TRU

  21. Determine whether the triangles are similar. If they are, explain why andwrite a similarity statement. T A R  J Yes, AA~ XTR ~ KAJ

  22. Find the length of BC. 7x = 20 20 7 x =

  23. Find the value of x. 4x = 70 x = 17.5 10 4

  24. 6.5 – Prove Triangles Similar by SSS and SAS

  25. Side-Side-Side Similarity (SSS~): Two triangles are similar if the 3 corresponding side lengths are proportional A D C F E B

  26. Side-Angle-Side Similarity (SAS~): Two triangles are similar if 2 corresponding sides are proportional and the included angle is congruent A D C F E B

  27. 1. Verify that ABC ~ DEF. Find the scale factor of ABC to DEF. ABC: AB = 12, BC = 15, AC = 9 DEF: DE = 8, EF = 10, DF = 6 A 9 D 12 Scale Factor: 8 6 C F 10 E B 15

  28. 2. Is either LMN or RST similar to ABC? Explain. ABC ~ RST by SSS~

  29. Determine whether the two triangles are similar. If they are similar, write a similarity statement and find the scale factor of Triangle B to Triangle A. Yes, SAS ~ L  X YXZ ~ JLK Scale Factor:

  30. Determine whether the two triangles are similar. If they are similar, write a similarity statement and find the scale factor of Triangle B to Triangle A. L  Z No

  31. Are the triangles similar? Explain your reasoning. GKH  NKM Yes, SAS ~

  32. Are the triangles similar? Explain your reasoning. ABC  DEC B  E Yes, AA ~

  33. Are the triangles similar? Explain your reasoning. No,

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