Proving Triangles Congruent - World of Teaching by yurtgc548

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```									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
In Lesson 4.2, 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
ABC   DEF
5.  B   E
6.  C   F
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
Side-Angle-Side (SAS)

1. AB  DE
2. A   D    ABC   DEF
3. AC  DF
included
angle
Included Angle
The angle between two sides

G          I           H
Included Angle

Name the included angle:
E

YE and ES     E
ES and YS     S

Y   S      YS and YE     Y
Angle-Side-Angle (ASA)

1. A   D
2. AB  DE     ABC   DEF
3.  B   E
include
d
side
Included Side
The side between two angles

GI          HI               GH
Included Side

Name the included angle:
E

Y and E   YE
E and S   ES
Y   S     S and Y   SY
Angle-Angle-Side (AAS)

1. A   D
2.  B   E   ABC   DEF
3. BC  EF
Non-included
side
Warning: No SSA Postulate

There is no such
thing as an SSA
postulate!

B               E

F
A      C
D

NOT CONGRUENT
Warning: No AAA Postulate
There is no such
thing as an AAA
postulate!

E
B

A     C                  F
D

NOT CONGRUENT
The Congruence Postulates
 SSS correspondence

 ASA correspondence

 SAS correspondence

 AAS   correspondence
 SSA correspondence

 AAA correspondence
Name That Postulate
(when possible)

SAS
ASA

SSA                 SSS
Name That Postulate
(when possible)

AAA
ASA

SAS                     SSA
Name That Postulate
(when possible)

Vertical
Angles
Reflexive
Property    SAS                    SAS

Vertical           Reflexive
Angles     SAS     Property    SSA
HW: Name That Postulate
(when possible)
HW: Name That Postulate
(when possible)
Let’s Practice
to enable us to apply the specified
congruence postulate.

For ASA:   B  D
For SAS:   AC  FE
For AAS:   A  F
HW
to enable us to apply the specified
congruence postulate.

For ASA:

For SAS:

For AAS:
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