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Honors Geometry
Mr. Rives U4D2
Name ___________________________
Date ____________ Period ________
ASA and AAS Triangle Congruence
Warm Up
1. Suppose TM  GL and M  G . What additional
information is needed to prove MTD  GLS by
SAS?
a. T  L
b. T  S
c.
TD  SL
d. MD  SG
S
T
M
D
G
L
2. Suppose TD  SG and MD  SL . What additional information is needed to prove the two
triangles congruent by SAS?
a. T  S
b. D  S
c. S  L
d. D  G
3. Suppose TD=10 cm, DM=9cm, TM=11 cm, SL=11 cm, and SG=9 cm. What else do you
need to know in order to prove that the two triangles are congruent by SSS?
a. LG= 9cm
b. TD=SL
c. GL= 10 cm
d. TM=SG
ASA Postulate:
If _________ __________ and the ___________ __________ of one triangle are congruent to
_____________ ______________ and the ___________ ___________ of another triangle, then the
two triangles are congruent.
Y
B
A
X
C
Z
AAS Theorem:
If two angles and a ____________________ __________ of one triangle are congruent to two
angles and a _________________ _____________ of another triangle, then the two triangles are
Y
B
congruent.
A
C
X
Z
1
Examples:
1. Which triangle is congruent to CAT by the ASA postulate?
a. DOG
b. INF
C
c. GDO
D
O
F
A
T
d. FNI
G
N
I
2. Can you conclude that INF is congruent to either of the other two triangles?
PROOFS:
X
A
1. Given: A  X , B  Y , BC  YZ
Prove: ABC  XYZ
B
Statements
C
Y
Z
reasons
2
2. Given: S  Q, RP bi sec ts SRQ
Prove: SRP  QRP
Statements
P
Q
S
Reasons
R
Q
3. Given: XQ || TR , XR bisects. QT
Prove: XMQ  RMT
X
Statements
M
R
Reasons
T
3
Ways to Prove Congruent Triangles
SSS
SAS
AAS
ASA
Triangle Classifications that do NOT prove Congruent
Triangles
AAA
SSA
Understanding the term INCLUDED for Triangles
Given 2 Sides and 1 Angle
Given 2 Angles and 1 Side
4
5