#### 4.3 Triangle Congruence by ASA and AAS

Download
Report

####
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