4.2 SSS and SAS Congruence
Date:
Goals:
• Prove triangles congruent by SSS
• Prove triangles congruent by SAS
Warm-up: Sketch a diagram showing two congruent triangles, ABC  QRS . If AB  15 ,
can we determine any of the side lengths of QRS ? Explain.
Side Side Side Congruence
Example 1: SSS Congruence
Determine if the following triangles can be proven congruent by SSS. If they cannot, state what is missing.
A.
B.
C.
10
U
E
F
F
R
C
8
15
15
10
I
A
L
H
16
16
D
B
8
12
N
12
G
K
Side Angle Side Congruence:
Included Angles:
Example 2: SAS Congruence
Determine if the following triangles can be proven congruent by SAS. If they cannot, state what is missing.
A
R
A. L
B.
C.
C
M
A
B
N
P
T
U
Example 3: Using SSS or SAS in Proofs
Complete the following proofs.
O
H
Q
F
P
A. Given: OP  EH , OH  EP
Prove: HOP  PEH
Statement
1. OP  EH , OH  EP
2. HP  HP
3. HOP  PEH
E
H
Reason
D
F
B. Given: FI  RG , FN  RN
R
N is the midpoint of IG
Prove: FIN  RGN
N
I
Statement
G
Reason
1. FI  RG , FN  RN
N is the midpoint of IG
2. IN  NG
3. FIN  RGN
C. Given: EN  NG , MN  NP
E
P
N
Prove: ENG  GNP
G
M
Statement
1. EN  NG , MN  NP
2. ENM  PNG
3.
Reason
N
D. Given: MN  MK ,
ML bisects NMK
L
Prove: MLN  MLK
M
K
Statement
Reason
1. MN  MK
ML bisects NMK
2. NML  KML
3.
4. MLN  MLK
E. Given: QT is a perpendicular bisector of UR
Q
Prove: QTU  QTR
U
Statement
1. QT is a perpendicular bisector of UR
2. QTU and QTR are right angles
3. QTU  QTR
4. UT  TR
5.
6. QTU  QTR
R
T
Reason