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Geo. Proofs 5-3
Proving Triangles
Similar
(AA, SSS, SAS)
Lesson 5-3: Proving Triangles
Similar
1
AA Similarity (Angle-Angle)
If 2 angles of one triangle are congruent to 2 angles of
another triangle, then the triangles are similar.
E
B
A
C
Given:
Conclusion:
D
A  D
F
and
B  E
ABC ~ DEF
Lesson 5-3: Proving Triangles
Similar
2
SSS Similarity (Side-Side-Side)
If the measures of the corresponding sides of 2 triangles
are proportional, then the triangles are similar.
E
B
5
A
Given:
10
8
11
C
D
AB BC
AC


DE
EF
DF
Conclusion:
16
22
F
8
5
11


16
22
10
ABC ~ DEF
Lesson 5-3: Proving Triangles
Similar
3
SAS Similarity (Side-Angle-Side)
If the measures of 2 sides of a triangle are proportional to the
measures of 2 corresponding sides of another triangle and the angles
between them are congruent, then the triangles are similar.
E
B
5
A
10
11
C
D
22
F
AB AC
Given: A  D and

DE DF
Conclusion:
ABC ~ DEF
Lesson 5-3: Proving Triangles
Similar
4
Proving Triangles Similar
Similarity is reflexive, symmetric, and transitive.
Steps for proving triangles similar:
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.
Lesson 5-3: Proving Triangles
Similar
5
Given : DE FG
Problem #1
Pr ove : DEC
FGC
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
G
Given
1. DE FG
AA
D
2. D  F
C
E
F
Alternate Interior <s
3. E  G Alternate Interior <s
4. DEC FGC AA Similarity
Lesson 5-3: Proving Triangles
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6
Problem
Given : IJ  3LN JK  3NP
#2 Pr ove : IJK LNP
IK  3LP
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
Statements
Reasons
Step 5: Is there more?
1. IJ = 3LN ; JK = 3NP ; IK = 3LP
Given
SSS
J
K
N
I
L
IJ
JK
IK
2.
=3,
=3,
=3
LN
NP
LP
P
IJ
JK
IK
3.
=
=
LN NP LP
4.
IJK~
LNP
Lesson 5-3: Proving Triangles
Similar
Division Property
Substitution
SSS Similarity
7
Given : G is the midpo int of ED
Problem #3
H is the midpo int of EF
Pr ove :
EGH
EDF
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………….
E
Step 5: Is there more?
G
H
D
Lesson 5-3: Proving Triangles
Similar
F
8
Statements
Reasons
1.
G is the Midpoint of ED
Given
H is the Midpoint of EF
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
ED
EF
Division Property
5.
EG
=2 and
EH
=2
Substitution
ED EF
6.
=
EG EH
7. GEHDEF
Reflexive Property
8. EGH~ EDF
SAS Postulate
Lesson 5-3: Proving Triangles
Similar
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