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Sections 4-4
Methods of Proving Triangles
Congruent
SSS
SAS
ASA
AAS
HL
If three sides of one triangle are congruent to three
sides of another triangle, the triangles are congruent.
If two sides and the included angle of one triangle are
congruent to the corresponding parts of another
triangle, the triangles are congruent.
If two angles and the included side of one triangle are
congruent to the corresponding parts of another
triangle, the triangles are congruent.
If two angles and the non-included side of one triangle
are congruent to the corresponding parts of another
triangle, the triangles are congruent.
If the hypotenuse and leg of one right triangle are
congruent to the corresponding parts of another right
triangle, the right triangles are congruent.
Congruent Triangles
Name the congruence
FRS 
Is
PQD ?
R
P
F
120°
120°

35°
35°
D
S
ASA
Q
Congruent Triangles
Name the congruence
Is
FRS

QSR ?
R
42°
F

42°
Q
Shared Side –
Reflexive Prop
S
SSA
WHY NOT?
SSA is NOT a valid
Triangle congruence
Congruent Triangles
Name the congruence
Is
FRS

QSR ?
R
50°

F
Q
50°
S
SAS
Shared Side –
Reflexive Prop
Congruent Triangles
Name the congruence
MNR 
Is
R
PTB ?
B
N
P

M
SSS ?
T
WHY NOT?
Names of the triangles in the congruence statement
are not in corresponding order.
A
C Writing a PROOF
B
1 2
E
SAS
Given: AB = BD
EB = BC
Prove: ∆ABE =
˜ ∆DBC
D
A
B
1
E
C
2
SAS
Given: AB = BD
EB = BC
Prove: ∆ABE ≅ ∆DBC
D
STATEMENTS
AB ≅ BD
<1 ≅ <2
EB ≅ BC
∆ABE ≅ ∆DBC
REASONS
Given
VA
Given
SAS
C
12
Given: CX bisects ACB
A≅ B
Prove: ∆ACX ≅∆BCX
AAS
A
X
B
CX bisects ACB
1≅ 2
A≅ B
CX ≅ CX
∆ACX ≅ ∆BCX
Given
Def of angle bisector
Given
Reflexive Prop
AAS
Can you prove these triangles
are congruent?
A
B Given: AB ll DC;
X is the midpoint of AC
Prove: AXB =
˜ CXD
X
D
C
A
B Given: AB ll DC
X is the midpoint of AC
Prove: AXB =
˜ CXD
X
D
C
ASA