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.
5. x = _______ x
12x = 160 40 3
x =

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

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.

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

13. Use the diagram to complete the statement.
11. x = _______ x
16x = 72
x = 4.5

14. Use the diagram to complete the statement.
12. y = _______
6y = 128 64 3
y =

15. 13. Determine whether the triangles are similar
13. Determine whether the triangles are similar. If they are, explain why and write a similarity statement.
47° No
26°

16. given Vertical angles ABC ~ EDC AA~ ABC  CDE ACB  ECD
13. Determine whether the triangles are similar. If they are, explain why and write a similarity statement.
given
ABC  CDE
Vertical angles
ACB  ECD
ABC ~ EDC
AA~

17. B  E given C  F  sum theorem ABC ~ DEF AA~ 77° 55°
13. Determine whether the triangles are similar. If they are, explain why and write a similarity statement.
B  E
given
77°
55°
C  F
 sum theorem
ABC ~ DEF
AA~

18. RUT  SVR Corresp. s RTU  VSR Corresp. s SRV ~ TRU AA~
13. Determine whether the triangles are similar. If they are, explain why and write a similarity statement.
RUT  SVR
Corresp. s
RTU  VSR
Corresp. s
SRV ~ TRU
AA~

19. 14. Find the length of BC.
7x = 20 20 7
x =

20. 15. Find the value of x. x 5 14 4 10 4

21. 15. Find the value of x.
4x = 70
x = 17.5 10 4

22. 6.5 – Prove Triangles Similar by SSS and SAS

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

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

25. 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 12 D
Scale Factor: 8 6 C E 10 F B 15

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

27. 3. Determine whether the two triangles are similar
3. 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  X
YES or NO
______ ~ ______
Scale Factor:
YXZ
JLK

28. 3. Determine whether the two triangles are similar
3. 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 or NO
______ ~ ______
Scale Factor:

29. GKH  NKM YES or NO Reason: ___________ SAS ~ 15 4 6 10
4. Determine whether the triangles are similar. If they are similar, state which postulate or theorem that justifies your answer. Show all work! 15 4 6 10
GKH  NKM
YES or NO
Reason: ___________
SAS ~

30. ABC  DEC B  E YES or NO Reason: ___________ AA ~
4. Determine whether the triangles are similar. If they are similar, state which postulate or theorem that justifies your answer. Show all work!
ABC  DEC
B  E
YES or NO
Reason: ___________
AA ~

31. YES or NO Reason: ___________
4. Determine whether the triangles are similar. If they are similar, state which postulate or theorem that justifies your answer. Show all work!
YES or NO
Reason: ___________