These slides are about the similarity of triangles. These contain all the slides that explain similar triangles.

1. 7.3
Proving
Triangles
Similar
(AA~, SSS~, SAS~)

2. Similar Triangles
Two triangles are similar if
they are the same shape. That
means the vertices can be
paired up, so the angles are
congruent. Size does not
matter.

3. AA Similarity
(Angle-Angle or AA~)
A  D
B  E
If 2 angles of one triangle are congruent to 2 angles of
another triangle, then the triangles are similar.
E
D
A
B
C
F
ABC~ DEF
Conclusion:
and
Given:
by AA~

4. SSS Similarity
(Side-Side-Side or SSS~)
ABC~ DEF
If the lengths of the corresponding sides of 2 triangles are
proportional, then the triangles are similar.
E
D
A
B
C
F
Given:
Conclusion:

BC
EF
AB
DE

AC
DF
by SSS~

5. E
D
A
B
C
F
Example: SSS Similarity
(Side-Side-Side)
Given:
Conclusion:
ABC~ DEF

BC
EF
AB
DE

AC
DF
5
11 22
8 16
10

8
16
5
10

11
22
By SSS ~

6. E
D
A
B
C
F
SAS Similarity
(Side-Angle-Side or SAS~)
ABC~ DEF
AB AC
A D and
DE DF
   
If the lengths of 2 sides of a triangle are proportional to the lengths
of 2 corresponding sides of another triangle and the included angles
are congruent, then the triangles are similar.
Given:
Conclusion: by SAS~

7. E
D
A
B
C
F
Example: SAS Similarity
(Side-Angle-Side)
Given: Conclusion:
ABC~ DEF
A  D
AB
DE

AC
DF
5
11 22
10
By SAS ~

8. A
B C
D E
80
80
ABC ~ ADE by AA ~ Postulate

9. A B
C
D E
CDE~ CAB by SAS ~ Theorem
6
3
10
5

10. O
N
L
K
M
KLM~ KON by SSS ~ Theorem
6
3
10
5
6
6
Slide from MVHS

11. C
B
A
D
ACB~ DCA by SSS ~ Theorem
24
36
20
30
16

12. N
L
A
P
LNP~ ANL by SAS ~ Theorem
25 9
15

13. Similarity is reflexive, symmetric, and transitive.
1. Mark the Given.
2. Mark …
Reflexive (shared) Angles or Vertical Angles
3. Choose a Method. (AA~, SSS~, SAS~)
Think about what you need for the chosen method and
be sure to include those parts in the proof.
Steps for proving triangles similar:
Proving Triangles Similar

14. Problem #1
:
Pr :
Given DE FG
ove DEC FGC
C
D
E
G
F
Step 1: Mark the given … and what it implies
Step 2: Mark the vertical angles
Step 3: Choose a method: (AA,SSS,SAS)
Step 4: List the Parts in the order of the method with reasons
Step 5: Is there more? Statements Reasons
Given
Alternate Interior <s
AA Similarity
Alternate Interior <s
1. DE FG
2. D F
  
3. E G
  
4. DEC FGC
AA

15. Problem #2
Step 1: Mark the given … and what it implies
Step 2: Choose a method: (AA,SSS,SAS)
Step 4: List the Parts in the order of the method with reasons
Step 5: Is there more? Statements Reasons
Given
Division Property
SSS Similarity
Substitution
SSS
: 3 3 3
Pr :
Given IJ LN JK NP IK LP
ove IJK LNP
  
N
L
P
I
J K
1. IJ = 3LN ; JK = 3NP ; IK = 3LP
2.
IJ
LN
=3,
JK
NP
=3,
IK
LP
=3
3.
IJ
LN
=
JK
NP
=
IK
LP
4. IJK~ LNP

16. Problem #3
Step 1: Mark the given … and what it implies
Step 3: Choose a method: (AA,SSS,SAS)
Step 4: List the Parts in the order of the method with reasons
Next Slide………….
Step 5: Is there more?
SAS
: midpoint
midpoint
Prove :
Given G is the of ED
H is the of EF
EGH EDF
E
D
F
G H
Step 2: Mark the reflexive angles

17. Statements Reasons
1. G is the Midpoint of
H is the Midpoint of
Given
2. EG = DG and EH = HF Def. of Midpoint
3. ED = EG + GD and EF = EH + HF Segment Addition Post.
4. ED = 2 EG and EF = 2 EH Substitution
Division Property
Substitution
Reflexive Property
SAS Postulate
ED
EF
7. GEHDEF
8. EGH~ EDF
6.
ED
EG
=
EF
EH
5.
ED
EG
=2 and
EF
EH
=2

18. Similarity is reflexive,
symmetric, and
transitive.

19. Choose a Problem.
Problem #1
Problem #2
Problem #3
End Slide Show
SSS
SAS
AA
C
E
G
F
D
E
D
F
G H
P
N
L
I
J K

20. The End
1. Mark the Given.
2. Mark …
Shared Angles or Vertical Angles
3. Choose a Method. (AA, SSS, SAS)
**Think about what you need
for the chosen method and
be sure to include
those parts in the proof.