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

B

A

C E

D

F

DF

AC

EF

BC

DE

AB

Side-Angle-Side Similarity (SAS~):

Two triangles are similar if 2 corresponding sides are proportional and the included angle is congruent

EF

BC

DE

AB

B

A

C E

D

F

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

B

A

C E

D

F

12

8

15

9

6

10

8

12

2

3

10

15

2

3

6

9

2

3

Scale Factor:2

3

2. Is either LMN or RST similar to ABC? Explain.

8

10

4

5

6

12

1

2

5

10

1

2

6

12

1

2

5

10

1

2ABC ~ RST by SSS~

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.

4

16

1

4

3

12

1

4

L X

YES or NO

______ ~ ______

Scale Factor:

YXZ JLK

1

4

10

18

2

9

9

16

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:

4. Determine whether the triangles are similar. If they are similar, state which postulate or theorem that justifies your answer. Show all work!

15

65

2

10

45

2

GKH NKM

SAS ~

4

106

15

YES or NOReason: ___________

ABC DEC

B E

YES or NOReason: ___________AA ~

4. Determine whether the triangles are similar. If they are similar, state which postulate or theorem that justifies your answer. Show all work!

16

24

2

3

28

36

7

9

YES or NOReason: ___________

4. Determine whether the triangles are similar. If they are similar, state which postulate or theorem that justifies your answer. Show all work!

∆HGJ ~ ∆HFKBy SSS~

#10

HW ProblemSecti

onPage # Assignment

Spiral

6.5 391-394 3-11, 15, 16, 33 (a & b only) 10 - 15

16.5

22

15

20

18

24

15

203

4

18

243

4

16.5

223

4