CPCTC
HOMEWORK: Lesson 4.6/1-9, 18
Chapter 4 Test - FRIDAY
PROVE IT!
CPCTC
Corresponding Parts of Congruent
Triangles are Congruent
CPCTC
• We say: Corresponding Parts of Congruent
Triangles are Congruent or CPCTC for short
• Once you have proven two triangles congruent
using one of the short cuts, the rest of the parts of
the triangle you haven’t proved directly are also
congruent!
1. Take the 1st Given and MARK it on the picture
2. Write this Given in the PROOF & its reason
(given)
1. If the Given is NOT a  stmt, write the 
stmt to match
Continue until there are no more Given
STEPS
TO
3. Do you have 3  stmts?
WRITE
1. If not, look for built-in parts
A
PROOF 4. Do you have  triangles?
1. If not, write CNBD
5. Write the triangle congruence and reason.
6. If the PROVE is a pair of corresponding parts
Write the congruency & CPCTC as the reason
CPCTC EXAMPLE
Given: TV  WV,
TW bisects UX
Prove: TU  WX
PROOF:
TV  WV
TW bisects UX
UV  VX
TVU  WVX
U
W
T
V
Given
Given
Definition of segment bisector
VA
ΔTUV  ΔWXV
SAS
TU  WX
CPCTC
X
MUST Prove
Triangles  1st,
before showing
corresponding
parts are 
Corresponding Parts of Congruent
Triangles are Congruent.
CPCTC
You can only use CPCTC in a proof
AFTER you have proven a
TRIANGLE congruence.
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.
GIVEN: 𝐴𝐶 ≅ 𝐷𝐹, <C ≅ <F, 𝐶𝐵 ≅ 𝐹𝐸
Prove: AB  DE
A
PROOF:
B
C
𝐴𝐶 ≅ 𝐷𝐹
given
<C ≅ <F
given
𝐶𝐵 ≅ 𝐹𝐸
given
D
∆𝑨𝑩𝑪 ≅ ∆𝑫𝑬𝑭
F
E
SAS
𝑨𝑩 ≅ 𝑫𝑬
CPCTC
GIVEN: JO  SH;
O IS THE MIDPOINT OF SH
PROVE: <S ≅ <H
PROOF:
JO  SH
S
0
H
given
< JOS ≅ < JOH
prop of  lines
O is the midpoint of SH given
SO ≅ OH
def of midpt
JO ≅ JO
J
reflexive prop
∆𝐒𝐎𝐉 ≅ ∆𝐇𝐎𝐉
SAS
∴<S ≅ <H
CPCTC
Given: BC bisects AD
A   D
Prove: AB  DC
A
C
2
1
E
B
D
PROOF:
BC bisects AD
AE  ED
given
def segment bisector
A   D
given
1   2
VA
∆𝐀𝐄𝐁 ≅ ∆𝑫𝑬𝑪
ASA
AB  DC
CPCTC