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

Use the diagram to complete the statement. x

Use the diagram to complete the statement. 8

Use the diagram to complete the statement. 5. x = _______ x 12x = 160 40 3 x =

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

Use the diagram to complete the statement. DEF

Use the diagram to complete the statement. BC DE FD

Use the diagram to complete the statement.

Use the diagram to complete the statement. x 16

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

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

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°

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~

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~

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~

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

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

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

6.5 – Prove Triangles Similar by SSS and SAS

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

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

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

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

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

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:

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 ~

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 ~

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: ___________