Transcript 4.3 Triangle Congruence by ASA and AAS

4.3 Triangle Congruence by
ASA and AAS
2 cards
Angle Side Angle Postulate
(ASA)

If two angles and the included side of
one triangle are congruent to two
angles and the included side of another
triangle, then the two triangles are
congruent.
E
If:
B
D
F
A
C
Then
ABC 
DEF
Angle Angle Side Theorem
AAS

If two angles and a non included side of
one triangle are congruent to two
angles and the corresponding side of
another triangle, then the triangles are
congruent
If:
E
B
D
F
A
C
Then
ABC 
DEF
Ex 1: Prove that the triangles
are congruent
A
Y
P
X
B
Ex 1: Prove that the triangles
are congruent
1. A  B
AP  BP
A
Y
P
X
B
Ex 1: Prove that the triangles
are congruent
1. A  B
AP  BP
A
Y
P
X
B
1.
Given
Ex 1: Prove that the triangles
are congruent
1. A  B
AP  BP
A
Y 2. APX  BPY
P
X
B
1.
Given
Ex 1: Prove that the triangles
are congruent
1. A  B
AP  BP
A
Y 2. APX  BPY
P
X
B
1.
2.
Given
Vertical angles are
congruent
Ex 1: Prove that the triangles
are congruent
1. A  B
AP  BP
A
1.
2.
Y 2. APX  BPY
P
3.
X
B
APX 
BPY
Given
Vertical angles are
congruent
Ex 1: Prove that the triangles
are congruent
1. A  B
AP  BP
A
1.
2.
Y 2. APX  BPY
3.
P
3.
X
B
APX 
BPY
Given
Vertical angles are
congruent
ASA
Ex 2: Prove the triangles are
congruent
A
B
D
C
Ex 2: Prove the triangles are
congruent
1. AB
CD, D  B
A
B
D
C
1.
Given
Ex 2: Prove the triangles are
congruent
1. AB
CD, D  B
2. BAC  DCA
A
B
D
C
1.
Given
Ex 2: Prove the triangles are
congruent
1. AB
CD, D  B
2. BAC  DCA
A
B
D
C
1.
2.
Given
Alternate interior
angles are
congruent
Ex 2: Prove the triangles are
congruent
1. AB
CD, D  B
2. BAC  DCA
3. AC  AC
A
B
D
C
1.
2.
Given
Alternate interior
angles are
congruent
Ex 2: Prove the triangles are
congruent
1. AB
CD, D  B
2. BAC  DCA
1.
2.
3. AC  AC
3.
A
B
D
C
Given
Alternate inerterior
angles are
congruent
Reflexive
Ex 2: Prove the triangles are
congruent
1. AB
CD, D  B
2. BAC  DCA
1.
2.
3. AC  AC
4.
ABC 
CDA
A
B
D
C
3.
Given
Alternate ineterior
angles are
congruent
Reflexive
Ex 2: Prove the triangles are
congruent
1. AB
CD, D  B
2. BAC  DCA
1.
2.
3. AC  AC
4.
ABC 
CDA
A
B
D
C
3.
4.
Given
Alternate ineterior
angles are
congruent
Reflexive
AAS
Ex 3: Prove the triangles are
congruent
XR bisects QT
Q
X
M
T
R