Download 10.1 Class Notes Congruent Tri Post and Theorems KEY

Class Notes
Date:
10.1 – CONGRUENT TRIANGLE POSTULATES AND THEOREMS
(SSS, SAS, ASA, AAS, and HL)
Side – Side – Side (SSS)
Prove
B
AB  DE
BC  EF
E
AC  DF
A
C
F
D
then ∆ABC  ∆DEF by SSS
Side – Angle – Side (SAS)
Prove
B
A  D
E
A
C
AC  DF
D
F
AB  DE
then ∆ABC  ∆DEF by SAS
Angle – Side – Angle (ASA)
Prove
B
A  C
AD  CD
Note that the side
marked is between
the two angles.
BDA  BDC
then ∆ABD  ∆CBD by
A
C
D
Angle – Angle – Side (AAS)
Prove
A
B  D
B
BCA  DCE
C
AC  EC
then ∆ABC  ∆EDC by
D
ASA
AAS
E
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Class Notes
Date:
Hypotenuse – Leg (HL) – must be a right triangle; must state right angle in proof
A
Prove
D
mC=90°, mF=90°
AB  DE
BC  EF
C
B
F
then ∆ABC  ∆DEF by
E
HL
Can the triangles be proved congruent? If so, name the postulate (SSS, SAS, or
ASA) or theorem (AAS or HL) that would prove the triangles congruent. If not,
write NONE. You must use the markings shown. The only markings that can be
added are shared sides or vertical angles.
1)
2)
3)
HL
AAS
SAS
4)
5)
6)
SSS
HL
AAS
7)
8)
9)
SAS
ASA
NONE
10)
11)
ASA
12)
AAS
AAS
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Class Notes
Date:
13)
14)
15)
AAS
NONE
SSS
What additional congruence statement is needed to prove the triangles
congruent by the indicated postulate or theorem?
K
Given: ∆JKM and ∆LKM
KM  KM
13) JK  LK , JM  LM by SSS
J  L
14) 1  2 , KM  KM by AAS
JM  LM
15) J  L , 1  2 by ASA
JM  LM
16) JK  LK , J  L by SAS
Given: ∆OPQ and ∆SRQ
1 2
M
J
L
P
O
OQ  SQ 17) OP  SR , PQ  RQ by SSS
1
Q
OQ  SQ 18) O  S , 1  2 by ASA
1  2
19) OQ  SQ , PQ  RQ by SAS
O  S
20) PQ  RQ , 1  2 by AAS
2
R
S
Use the given information to determine if the triangles below are congruent.
If so, which congruence postulate or theorem would you use?
21) Given: C is the midpoint of SU .
DU  KS
Is DUC  KSC ? NO
D
C
U
S
K
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