What do we need to determine
two triangles are congruent?
Agenda:
• CPCTC warmup
• SSS, SAS, ASA notes/practice
• AAS and HL tomorrow
• Practice all Wednesday
• Triangle TEST Friday
5 ways to prove triangles
congruent
•
•
•
•
•
SSS
SAS
ASA
AAS
HL
SSS Postulate – If three sides of
one triangle are congruent to three
sides of another triangle, then the
triangles are congruent.
S – Side
D
B
A
S – Side
C F
S - Side
S: AB @ FD
S: BC @ DE
S: AC @ FE
E
DABC @ DFDE
because of SSS
B
What SSS Looks Like…
R
F
C
A
E
S: AB @ ED
S: BC @ EF
S: AC @ FD
DABC @ DDEF
D
P
Q
S
DPRQ @ DSRQ
S: PR @ SR
S: PQ @ SQ
S: RQ @ RQ
SAS Postulate – If two sides and the
included angle of one triangle are congruent
to two sides and the included angle of
another triangle, then the triangles are
congruent.
S – Side
A – Angle S - Side
D
B
S: AB @ FD
A: B @ D
S: BC @ DE
DCAB @ DEFD
A
C F
E
because of SAS
Y
What SAS Looks Like…
S: WT @ YZ
A: W @ Z
S: WV @ ZX
T
X
W
Z
V
DYZX @ DTWV
M
L
N
P
DLMN @ DQPN
Q
S: MN @ PN
A: LNM @ QNP
S: LN @ QN
What SAS Does NOT Look Like…
Y
T
W
V
X
Z
The angle pair that is marked congruent
MUST be in between the two congruent
sides to use SAS! There is NOT enough
information to determine whether these
triangles are congruent.
ASA Postulate – If two angles and the
included side of one triangle are congruent
to two angles and the included side of
another triangle, then the triangles are
congruent.
A – Angle S – Side
A: B @ D
S: AB @ FD
A: A @ F
D
B
A - Angle
DACB @ DFED
A
C F
E
because of ASA
What ASA Looks Like…
D
H
A: N @ R
S: MN @ PR
A: M @ P
DMNL @ DPRQ
F
G
J
Q
L
DFDG @ DJHG
A: D @ H
S: DG @ HG
A: DGF @ HGJ
P
M
N
R
What ASA Does NOT Look Like…
L
M
Q
N
P
R
The pair of sides pair that are
marked congruent MUST be in
between the two congruent angles
to use ASA!
Practice
• Textbook p. 245 #9 – 26
• Textbook p. 254 #10 – 14, 16, 17, 19, 21
Determine what is missing in
order to use the indicated reason