Honors Geometry 14 Nov 2011
Take papers from your folder and put them in your binder.
Place your binder, HW and text on your desk.
YOUR FOLDERS SHOULD BE EMPTY
EXCEPT FOR YOUR WARM UP PAPER and current day’s
classwork
Warm-up- silently please 
1)read page 232.
Answer in a complete sentence on your warm–up
paper:
what does CPCTC mean?
2)do pg. 230, # 11
Objective
Students will review congruency shortcuts and
use CPCTC to prove congruency
Students will view a powerpoint presentation,
take notes and work independently and with
their group to solve problems.
Homework due today
none
Homework due Nov. 15
P1- extension-pg. 224: 1-21 odds
Pg. 229: 2 – 20 evens
TEST- Nov 16/17
Study: constructions, isosceles triangle properties,
triangle sum, triangle inequalities, triangle
congruency shortcuts
Chapter 4 Triangles
Term
Definition
SSS
Congruence
Shortcut
SAS
Congruence
Shortcut
SSA
If three sides of one triangle
are congruent to three sides of
another triangle, then the
triangles are congruent
If two sides and the included
angle of one triangle are
congruent to two sides and the
included angle of another
triangle, then the triangles are
congruent
DOES NOT guarantee
congruency
Example- add notation
(conguency marks)
not a nice word if you
spell it backwards =
NO guaranteed
congruency!!!
90o
Chapter 4 Triangles-Term
Definition
ASA
Congruence
Shortcut
SAA
Congruence
Shortcut
AAA
Example
If two angles and the included
side of one triangle are
congruent to two angles and
the included side of another
triangle, then the triangles are
congruent.
If two angles and a nonincluded side of one triangle
are congruent to the
corresponding two angles and
non-included side of another
triangle, then the triangles are
congruent
DOES NOT guarantee
congruency
90o
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 previous lessons, 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
ABC   DEF
3. AC  DF
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
include
d
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
Nonincluded
side
Warning: No SSA Postulate
There is no such
thing as an SSA
postulate!
E
B
F
A
C
D
NOT necessarily CONGRUENT
Warning: No AAA Postulate
There is no such
thing as an AAA
postulate!
E
B
A
C
D
F
NOT necessarily CONGRUENT
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
ASA
SAS
SSA
Name That Postulate
(when possible)
take notes…
Reflexive
Property
Vertical
Angles
SAS
Vertical
Angles
SAS
SAS
Reflexive
Property
SSA
CW: Name That Postulate
(when possible)
CW: 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
CW
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.
Corresponding parts
When you use a shortcut (SSS, AAS, SAS, ASA, HL)
to show that 2 triangles are  ,
that means that ALL the corresponding parts are
congruent.
EX: If a triangle is congruent by ASA (for instance),
then all the other corresponding parts are  .
B
F
That means that EG  CB
A
E
C
What is AC congruent to?
G
FE
Corresponding parts of congruent
triangles are congruent.
Corresponding parts of congruent
triangles are congruent.
Corresponding parts of congruent
triangles are congruent.
Corresponding Parts of Congruent
Triangles are Congruent.
CPCTC
If you can prove
congruence using a
shortcut, then you
KNOW that the
remaining
corresponding parts are
congruent.
You can only use
CPCTC in a proof
AFTER you have
proved
congruence.
A
Prove: AB
 DE
Statements
B
C
⦟C  ⦟ F
D
F
AC  DF
E
Reasons
Given
Given
CB  FE
Given
ΔABC ΔDEF
SAS
AB  DE
CPCTC
EXAMPLE 2
Use the SAS Congruence Postulate
CW: Write a proof.
GIVEN
BC
PROVE
DA, BC AD
ABC
CDA
STATEMENTS
S
REASONS
1.
BC
DA
1.
Given
2.
BC
AD
2.
Given
3.
Alternate Interior Angles
Theorem
4.
Reflexive Property of
Congruence
A
3.
S
4.
BCA
AC
DAC
CA
EXAMPLE 2
Use the SAS Congruence Postulate
STATEMENTS
5.
ABC
REASONS
CDA
5. SAS Congruence Postulate
debrief
what did you learn today?
what was easy? what was difficult?
what can I do to help you?