Title: G.7 Proving Triangles Similar
1G.7ProvingTrianglesSimilar
(AA, SSS, SAS)
2Similar 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.
3AA Similarity (Angle-Angle or AA)
If 2 angles of one triangle are congruent to 2
angles of another triangle, then the triangles
are similar.
and
Given
Conclusion
by AA
4SSS Similarity (Side-Side-Side or SSS)
If the lengths of the corresponding sides of 2
triangles are proportional, then the triangles
are similar.
Given
Conclusion
by SSS
5Example SSS Similarity (Side-Side-Side)
Conclusion
By SSS
6SAS Similarity (Side-Angle-Side or SAS)
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
7Example SAS Similarity (Side-Angle-Side)
Conclusion
By SAS
8A
80?
D
E
80?
B
C
?ABC ?ADE by AA Postulate
Slide from MVHS
9C
6
10
D
E
5
3
A
B
?CDE ?CAB by SAS Theorem
Slide from MVHS
10L
5
3
M
6
6
N
K
6
10
O
?KLM ?KON by SSS Theorem
Slide from MVHS
11A
20
D
30
24
16
B
C
36
?ACB ?DCA by SSS Theorem
Slide from MVHS
12L
15
P
A
25
9
N
?LNP ?ANL by SAS Theorem
Slide from MVHS
13Similarity is reflexive, symmetric, and
transitive.
Proving Triangles Similar
Steps for proving triangles similar
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.
14Problem 1
Step 1 Mark the given and what it implies
Step 2 Mark the vertical angles
AA
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 lts
Alternate Interior lts
AA Similarity
15Problem 2
Step 1 Mark the given and what it implies
SSS
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
1. IJ 3LN JK 3NP IK 3LP
Division Property
Substitution
SSS Similarity
16Problem 3
Step 1 Mark the given and what it implies
Step 2 Mark the reflexive angles
SAS
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?
17Statements Reasons
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
18Similarity is reflexive, symmetric, and
transitive.
19Choose a Problem.
End Slide Show
Problem 1
AA
Problem 2
SSS
Problem 3
SAS
20Problem 1
21Step 1 Mark the Given
and what it implies
22Step 2 Mark . . .
- Reflexive Angles
- Vertical Angles
if they exist.
23Step 3 Choose a Method
AA SSS SAS
24(No Transcript)
25Choose a Problem.
End Slide Show
Problem 1
AA
Problem 2
SSS
Problem 3
SAS
26Problem 2
27STATEMENTS
REASONS
1. Given
2. Division Prop.
3. Substitution
4. SSS Similarity
28Choose a Problem.
End Slide Show
Problem 1
AA
Problem 2
SSS
Problem 3
SAS
29Problem 3
30 and what it implies
Step 1 Mark the Given
31- Reflexive Angles
- Vertical Angles
Step 2 Mark . . .
32Step 3 Choose a Method
AA SSS SAS
33STATEMENTS
REASONS
1. Given
2. Def. of Midpoint
3. Seg. Add. Post.
4. Substitution
34STATEMENTS
REASONS
4. Substitution
5. Division Prop.
6. Substitution
7. Reflexive Prop
8. SAS Similarity
35The 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.