Transcript Geom-5.5-5.6-SSS-SAS-ASA

5-5 & 5-6
SSS, SAS, ASA, & AAS
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
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
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
ABC   DEF
3.  B   E
included
side
Included Side
The side between two angles
GI
HI
GH
Included Side
Name the included side:
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
ABC   DEF
3. BC  EF
Non-included
side
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
HW
Indicate the additional information needed
to enable us to apply the specified
congruence postulate.
For ASA:
For SAS:
For AAS:
Write a congruence statement for each
pair of triangles represented.
D
B
A
E
C
F
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Before we start…let’s get a few things straight
C
A
Y
B
X
INCLUDED SIDE
Z
Angle-Side-Angle (ASA)
Congruence Postulate
Two angles and the INCLUDED side
Angle-Angle-Side (AAS)
Congruence Postulate
Two Angles and One Side that is
NOT included
}
Your Only Ways
To Prove
Triangles Are
Congruent
Things you can mark on a triangle when they aren’t
marked.
Overlapping sides are
congruent in each
triangle by the
REFLEXIVE property
Vertical
Angles are
congruent
Alt Int
Angles are
congruent
given
parallel lines
Ex 1
In ΔDEF and ΔLMN , D  N , DE  NL and
E  L. Write a congruence statement.
 DEF   NLM
Ex 2
What other pair of angles needs to be
marked so that the two triangles are
congruent by AAS?
D
E  N
L
M
F
E
N
Ex 3
What other pair of angles needs to be
marked so that the two triangles are
congruent by ASA?
D
D  L
L
M
F
E
N
Determine if whether each pair of triangles is congruent by
SSS, SAS, ASA, or AAS. If it is not possible to prove that they
are congruent, write not possible.
Ex 4
G
K
I
H
J
ΔGIH  ΔJIK by
AAS
Determine if whether each pair of triangles is congruent by
SSS, SAS, ASA, or AAS. If it is not possible to prove that they
are congruent, write not possible.
Ex 5
B
A
C
D
E
ΔABC  ΔEDC by
ASA
Determine if whether each pair of triangles is congruent by
SSS, SAS, ASA, or AAS. If it is not possible to prove that they
are congruent, write not possible.
Ex 6
E
A
C
B
D
ΔACB  ΔECD by
SAS
Determine if whether each pair of triangles is congruent by
SSS, SAS, ASA, or AAS. If it is not possible to prove that they
are congruent, write not possible.
Ex 7
J
M
K
L
ΔJMK  ΔLKM by SAS or
ASA
Determine if whether each pair of triangles is congruent by
SSS, SAS, ASA, or AAS. If it is not possible to prove that they
are congruent, write not possible.
Ex 8
J
T
K
L
V
Not possible
U
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