Download 4-2: Triangle Congruence by SSS and SAS 4

4‐2: Triangle Congruence by SSS and SAS
4‐3: Triangle Congruence by ASA and AAS
4‐4: Using Corresponding Parts of Congruent Triangles
Side‐Side‐Side (SSS)
 If, in two triangles:
 three sides of one are congruent to three sides of the other, then the triangles are congruent.
E
B
F
C
A
D
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Side‐Angle‐Side (SAS)
 If, in two triangles:
 two sides and the included angle of one are congruent to two sides and the included angle of the other, then the triangles are congruent
E
B
F
C
D
A
Angle‐Side‐Angle (ASA)
 If, in two triangles:
 two angles and the included side of one are congruent to two angles and the included side of the other, then the two triangles are E
congruent.
B
F
C
A
D
2
Angle‐Angle‐Side (AAS)
 If, in two triangles:
 two angles and a non‐included side of one are congruent respectively to two angles and the corresponding non‐included side of the other, then the triangles are congruent.
E
B
F
C
D
A
Using only the given information, which pairs of triangles are congruent? Justify your answer.
1.
2.
No
Yes; SAS
3.
No
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Writing Proofs
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congruent
 Prove ___ parts of one triangle are ____________ to the _________________ parts of another corresponding
triangle.
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 Use Triangle Congruence Theorems and other theorems in the proof.
Ex. 1
Given: N is the midpoint of UC
F
C
N
U  C
Prove:
FUN  ACN
Statement
1). N is the midpoint of UC
U
A
Reason
1). Given
U  C
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Ex. 2
Given: mPLT  90, mLTO  90
and LP  TO
Prove: LTO  TLP
Statement
1). mPLT  90, mLTO  90
P
L
T
O
Reason
1). Given
and LP  TO
A
Ex. 3

Given: AE bisects BAD
B  D
Prove: ABC  ADC
Statement

1). AE bisects BAD
B  D
B
C
D
E
Reason
1). Given
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Ex. 4
K
 
Given: KJ ML and KJ  LM
Prove: KJL  LMK
Statement
 
1). KJ ML and KJ  LM
M
J
L
Reason
1). Given
Corresponding Parts of Congruent Figures are Congruent (CPCFC)
 If two figures are congruent, then so are all of their corresponding parts.
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Ex. 5
W
2
Given: 1  3; 2  4
Prove: WA  IT
Statement
1). 1  3; 2  4
A
1
3 4
T
I
Reason
1). Given
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