Triangle Congruence Proofs
undefined
Proving Triangles
Congruent
Two geometric figures with
exactly the
same size and
shape.
T
T
h
h
e
e
I
I
d
d
e
e
a
a
o
o
f
f
a
a
C
C
o
o
n
n
g
g
r
r
u
u
e
e
n
n
c
c
e
e
How much do you
How much do you
need to know. . .
need to know. . .
. . . about two triangles
to prove that they
are congruent?
In Lesson 4.2, you learned that if all
six pairs of corresponding parts (sides
and angles) are congruent, then the
triangles are congruent.
C
C
o
o
r
r
r
r
e
e
s
s
p
p
o
o
n
n
d
d
i
i
n
n
g
g
P
P
a
a
r
r
t
t
s
s
ABC
DEF
D
D
o
o
y
y
o
o
u
u
n
n
e
e
e
e
d
d
a
a
l
l
l
l
s
s
i
i
x
x
?
?
NO !
S
S
i
i
d
d
e
e
-
-
S
S
i
i
d
d
e
e
-
-
S
S
i
i
d
d
e
e
(
(
S
S
S
S
S
S
)
)
S
S
i
i
d
d
e
e
-
-
A
A
n
n
g
g
l
l
e
e
-
-
S
S
i
i
d
d
e
e
(
(
S
S
A
A
S
S
)
)
1.
AB
DE
2.
A
D
3.
AC
DF
ABC
DEF
B
A
C
E
D
F
included
angle
The angle
between
two sides
I
I
n
n
c
c
l
l
u
u
d
d
e
e
d
d
A
A
n
n
g
g
l
l
e
e
G
I
H
Name the
included
angle:
Y
E
and
E
S
E
S
and Y
S
Y
S and
Y
E
I
I
n
n
c
c
l
l
u
u
d
d
e
e
d
d
A
A
n
n
g
g
l
l
e
e
E
S
Y
A
A
n
n
g
g
l
l
e
e
-
-
S
S
i
i
d
d
e
e
-
-
A
A
n
n
g
g
l
l
e
e
(
(
A
A
S
S
A
A
)
)
1.
A
D
2.
AB
DE
3.
B
E
ABC
DEF
B
A
C
E
D
F
include
d
side
The side
between
two angles
I
I
n
n
c
c
l
l
u
u
d
d
e
e
d
d
S
S
i
i
d
d
e
e
GI
HI
GH
Name the
included
angle:
Y and
E
E and
S
S and
Y
I
I
n
n
c
c
l
l
u
u
d
d
e
e
d
d
S
S
i
i
d
d
e
e
YE
ES
SY
A
A
n
n
g
g
l
l
e
e
-
-
A
A
n
n
g
g
l
l
e
e
-
-
S
S
i
i
d
d
e
e
(
(
A
A
A
A
S
S
)
)
1.
A
D
2.
B
E
3.
BC
EF
ABC
DEF
B
A
C
E
D
F
Non-included
side
Warning:
Warning:
No SSA Postulate
No SSA Postulate
A
C
B
D
E
F
NOT CONGRUENT
There is no such
thing as an SSA
postulate!
Warning:
Warning:
No AAA Postulate
No AAA Postulate
A
C
B
D
E
F
There is no such
thing as an AAA
postulate!
NOT CONGRUENT
The Congruence Postulates
The Congruence Postulates
Name That Postulate
Name That Postulate
SAS
SAS
ASA
ASA
SSS
SSS
SSA
SSA
(when possible)
Name That Postulate
Name That Postulate
(when possible)
ASA
ASA
SAS
SAS
AAA
AAA
SSA
SSA
Name That Postulate
Name That Postulate
(when possible)
SAS
SAS
SAS
SAS
SAS
SAS
Reflexive
Property
Vertical
Angles
Vertical
Angles
Reflexive
Property
SSA
SSA
HW: Name That Postulate
HW: Name That Postulate
(when possible)
(when possible)
HW: Name That Postulate
HW: Name That Postulate
Let’s Practice
Let’s Practice
Indicate the additional information needed
to enable us to apply the specified
congruence postulate.
For ASA:
For SAS:
B
D
For AAS:
A
F
HW
HW
Indicate the additional information needed
to enable us to apply the specified
congruence postulate.
For ASA:
For SAS:
For AAS:
This powerpoint was kindly donated to
www.worldofteaching.com
http://www.worldofteaching.com
is home to over a
thousand powerpoints submitted by teachers. This is a
completely free site and requires no registration. Please
visit and I hope it will help in your teaching.
Exploring the concept of proving triangles congruent, this content covers the different criteria such as SAS, SSS, ASA, AAS, and the warning against using the SSA postulate. Corresponding parts, included angles, and sides, along with visual aids, help grasp the key principles to demonstrate triangle congruence.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
E N D
Presentation Transcript
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 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 H G I
Included Angle Name the included angle: E YE and ES ES and YS YS and YE E S Y Y S
Angle-Side-Angle (ASA) 1. A D 2. AB DE 3. B E ABC DEF include d side
Included Side The side between two angles GI GH HI
Included Side Name the included angle: E Y and E E and S S and Y YE ES SY Y S
Angle-Angle-Side (AAS) 1. A D 2. B E 3. BC EF ABC DEF 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 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 SSA SAS
Name That Postulate (when possible) Vertical Angles Reflexive Property SAS SAS Reflexive PropertySSA Vertical Angles SAS
HW: Name That Postulate (when possible)
HW: Name That Postulate (when possible)
Lets Practice Indicate the additional information needed to enable us to apply the specified congruence postulate. B D AC FE For ASA: For SAS: A F For AAS:
HW Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:
This powerpoint was kindly donated to www.worldofteaching.com http://www.worldofteaching.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.
