Download Proving triangles congruent

4.4 & 4.5
Proving Triangles
Congruent
Interactive notebook
Entries
• Pg. 17 4-4 & 4-5: Proving Triangles
Congruent
• Pg. 18 Proving Triangles Congruent
(Practice)
Objectives:
• Use the SSS, SAS, ASA, AAS
and HL postulates to test for
triangle congruence.
Corresponding Parts
In Lesson 4.3, you learned that if all
six pairs of corresponding parts (sides
and angles) are congruent, then the
triangles are congruent.
1. AB  DE
2. BC  EF
3. AC  DF
4.  A   D
5.  B   E
6.  C   F
ABC   DEF
Do you need all six ?
NO !
SSS
SAS
ASA
AAS
HL
Side-Side-Side (SSS)
1. AB  DE
2. BC  EF
3. AC  DF
ABC   DEF
Side-Angle-Side (SAS)
1. AB  DE
2. A   D
3. AC  DF
ABC   DEF
included
angle
Included Angle
The angle between two sides
G
I
H
Angle-Side-Angle (ASA)
1. A   D
2. AB  DE
ABC   DEF
3.  B   E
included
side
Included Side
The side between two angles
GI
HI
GH
Angle-Angle-Side (AAS)
1. A   D
2.  B   E
ABC   DEF
3. BC  EF
Non-included
side
Hypotenuse-Leg (HL)
A
B
1. AC  ZX
2. BC  YX
Z
C
X
Y
ABC   ZYX
RIGHT
TRIANGLES
Warning: No SSA Postulate
There is no such
thing as an SSA
postulate!
E
B
F
A
C
D
NOT ALWAYS CONGRUENT
Warning: No AAA Postulate
There is no such
thing as an AAA
postulate!
E
B
A
C
D
NOT ALWAYS CONGRUENT
F
The Congruence Postulates
SSS correspondence
ASA correspondence
SAS correspondence
AAS correspondence
HL correspondence
SSA correspondence
AAA correspondence
Name That Postulate
(when possible)
SAS
SSA
ASA
SSS
Name That Postulate
(when possible)
AAA
SAS
ASA
SSA
Name That Postulate
(when possible)
Reflexive
Property
SAS
Vertical
Angles
SAS
Vertical
Angles
SAS
Reflexive
Property
SSA