G.7 Proving Triangles Similar

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G.7ProvingTrianglesSimilar
(AA, SSS, SAS)
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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.
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AA 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
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SSS 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
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Example SSS Similarity (Side-Side-Side)

• Given

Conclusion
By SSS
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SAS 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
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Example SAS Similarity (Side-Angle-Side)
Conclusion

• Given

By SAS
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A
80?
D
E
80?
B
C
?ABC ?ADE by AA Postulate
Slide from MVHS
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C
6
10
D
E
5
3
A
B
?CDE ?CAB by SAS Theorem
Slide from MVHS
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L
5
3
M
6
6
N
K
6
10
O
?KLM ?KON by SSS Theorem
Slide from MVHS
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A
20
D
30
24
16
B
C
36
?ACB ?DCA by SSS Theorem
Slide from MVHS
12
L
15
P
A
25
9
N
?LNP ?ANL by SAS Theorem
Slide from MVHS
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Similarity 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.
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Problem 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
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Problem 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
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Problem 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?
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Statements 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
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Similarity is reflexive, symmetric, and
transitive.
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Choose a Problem.
End Slide Show
Problem 1
AA
Problem 2
SSS
Problem 3
SAS
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Problem 1
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Step 1 Mark the Given
and what it implies
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Step 2 Mark . . .

• Reflexive Angles
• Vertical Angles

if they exist.
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Step 3 Choose a Method
AA SSS SAS
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(No Transcript)
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Choose a Problem.
End Slide Show
Problem 1
AA
Problem 2
SSS
Problem 3
SAS
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Problem 2
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STATEMENTS
REASONS
1. Given
2. Division Prop.
3. Substitution
4. SSS Similarity
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Choose a Problem.
End Slide Show
Problem 1
AA
Problem 2
SSS
Problem 3
SAS
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Problem 3
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and what it implies
Step 1 Mark the Given
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• Reflexive Angles
• Vertical Angles

Step 2 Mark . . .
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Step 3 Choose a Method
AA SSS SAS
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STATEMENTS
REASONS
1. Given
2. Def. of Midpoint
3. Seg. Add. Post.
4. Substitution
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STATEMENTS
REASONS
4. Substitution
5. Division Prop.
6. Substitution
7. Reflexive Prop
8. SAS Similarity
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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.