Proving Triangles are Congruent
ASA and AAS
Chapter 4.5
Objectives: To use the ASA and AAS Theorem to prove that triangles are congruent
ASA   Theorem
• If two angles and the
included side of one triangle,
are congruent to the
corresponding angles and side
in a second triangle, then the
triangles are congruent.
ABC  XYZ — Why?
Y
B
X
A
C
ASA   Theorem
Z
Use ASA in Proofs
Write a two-column proof.
Step
L is the midpoint of WE
WL  LE
WR // ED
W  E
RLW  DLE
WRL  EDL
Reason
Given
Def of Midpt.
Given
Alternate Int.  Thm.
Vertical  Thm.
ASA   Thm.
Write a two-column proof.
Step
AB // CD; BC // DA
CBD  ADB
CDB  ABD
Reason
Given
Alternate Int.  Thm.
Alternate Int.  Thm.
BD  BD
Reflexive Property
ABD  CDB
ASA   Theorem.
AAS   Theorem
• If two angles and a nonincluded side of one
triangle, are congruent to
the corresponding angles
and side in a second
triangle, then the triangles
are congruent.
ABC  XYZ — Why?
Y
B
X
A
C
AAS   Theorem
Z
Write a two-column proof.
JNM  KNL
K
J
IMPORTANT HINT:
When you are given
overlapping triangles,
draw them separately.
L
M
N
N
K
J
M L
N
N
Step
NKL  NJM
KL  JM
JNM  KN L
JNM  KNL
Reason
Given
Given
Reflexive Property
AAS   Thm.
Homework
Chapter 4-5
• Pg 238
1-4, 8, 9, 15, 27
These are all
two-column proofs!!!
Video B
7:40-
Interactive Lab:
Proofs and Congruent Triangles