Download Side - Angle

Section 4.4
ASA AND AAS CONGRUENCE METHODS
USING CONGRUENCE POSTULATES AND THEOREMS
ASA AND AAS CONGRUENCE METHODS
Recall,
If
If all six pairs of corresponding parts (sides and angles) are
congruent, then the triangles are congruent.
Sides are
congruent
and
Angles are
congruent
1. AB
DE
4.
A
D
2. BC
EF
5.
B
E
3. AC
DF
6.
C
F
then
Triangles are
congruent
 ABC
 DEF
ASA AND AAS CONGRUENCE METHODS
POSTULATE
Angle - Side - Angle (ASA) Congruence Postulate
If two angles and the included side of one triangle are
congruent to two angles and the included side of a second
triangle, then the two triangles are congruent.
If
A
S
A
Angle
Side
Angle
N R
NP  RS
P S
then  MNP
 QRS
ASA AND AAS CONGRUENCE METHODS
The ASA Congruence Postulate is a shortcut for proving
two triangles are congruent without using all six pairs
of corresponding parts.
ASA AND AAS CONGRUENCE METHODS
Theorem
Angle-Angle-Side (AAS) Congruence Theorem
If two angles and a nonincluded side of one triangle are
congruent to two angles and the corresponding nonincluded
side of a second triangle, then the two triangles are
congruent.
If
A
A
S
Angle
Angle
Side
S Y
Q X
PQ WX
then  PQS
WXY
ASA AND AAS CONGRUENCE METHODS
The AAS Congruence Postulate is a shortcut for proving
two triangles are congruent without using all six pairs
of corresponding parts.
Example #1
Is it possible to prove that the triangles are congruent?
Explain why or why not.
C
E
H
I
D
G
F
K
J
Example #2
Given: B C,D F
M is the midpoint of DF.
Prove: BDM  CFM
C
B
D
M
F
Example #3
When searching for a missing airplane, searchers used
observations from people in two different areas of the
city. As shown, the observers were able to describe sight
lines from observers in different houses. One sightline
was from observers in House A and the other sightline
was from observers in House B. Assuming the sightlines
are accurate, did the searchers have enough information
to locate the airplane?
House A
Plane P
House B
HOMEWORK
p 223 8-13, 18-20,
23, 32, 35