Download Included Angle

Proving Triangles
Congruent
The Idea of a Congruence
Two geometric figures with
exactly the same size and
shape.
F
B
A
C
E
D
How much do you
need to know. . .
. . . about two triangles
to prove that they
are congruent?
Corresponding Parts
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
Side-Side-Side (SSS)
1. AB  DE
2. BC  EF
ABC   DEF
3. AC  DF
If 3 sides of one triangle are congruent to 3 sides of
another triangle, then the triangles are congruent
Side-Angle-Side (SAS)
1. AB  DE
2. A   D
3. AC  DF
ABC   DEF
included
side
If two sides and the included angle of one triangle are
congruent to two sides and the included angle of
another triangle, then the two triangles are congruent
Included Angle
The angle between two sides
G
I
H
Included Angle
Name the included angle:
E
Y
S
YE and ES
E
ES and YS
S
YS and YE
Y
Angle-Side-Angle (ASA)
1. A   D
2. AB  DE
3.  B   E
ABC   DEF
included
side
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.
Included Side
The side between two angles
GI
HI
GH
Included Side
Name the included angle:
E
Y
S
Y and E
YE
E and S
ES
S and Y
SY
Angle-Angle-Side (AAS)
1. A   D
2.  B   E
3. BC  EF
ABC   DEF
Non-included
side
If 2 angles and a non-included side of 1 triangle are
congruent to 2 angles and the corresponding nonincluded side of another triangle, then the 2 triangles
are congruent
Warning: No SSA Postulate
There is no such
thing as an SSA
postulate!
E
B
F
A
C
D
NOT CONGRUENT
Warning: No AAA Postulate
There is no such
thing as an AAA
postulate!
E
B
A
C
D
NOT CONGRUENT
F
The Congruence Postulates
 SSS
correspondence
 ASA
correspondence
 SAS
correspondence
 AAS
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
HW: Name That Postulate
(when possible)
HW: Name That Postulate
(when possible)
Let’s Practice
Indicate the additional information needed
to enable us to apply the specified
congruence postulate.
For ASA:
B  D
For SAS:
AC  FE
For AAS:
A  F
Indicate the additional information needed
to enable us to apply the specified
congruence postulate.
For ASA:
For SAS:
For AAS: