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
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
A
D
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
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
A
D
Using only the given information, which pairs of
triangles are congruent? Justify your answer.
1.
2.
No
Yes; SAS
3.
No
Writing Proofs
3
congruent
 Prove ___ parts of one triangle are ____________
to the _________________
parts of another
corresponding
triangle.
3
 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  C
U
A
Reason
1). Given
Ex. 2
L
Given: mPLT  90, mLTO  90
and LP  TO
Prove: LTO  TLP
Statement
1). mPLT  90, mLTO  90
and LP  TO
P
T
O
Reason
1). Given
A
Ex. 3
Given: AE bisects BAD
B  D
Prove: ABC  ADC
Statement
1). AE bisects BAD
B  D
B
C
E
Reason
1). Given
D
Ex. 4
K
J
Given: KJ ML and KJ  LM
Prove: KJL  LMK
Statement
1). KJ ML and KJ  LM
M
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.
Ex. 5
W
2
Given: 1  3; 2  4
Prove: WA  IT
Statement
1). 1  3; 2  4
A
1
3
T
Reason
1). Given
4
I