CPCTC sounds like a very difficult thing but it
really isn't it is kind of simple the only thing you
need to now is that !!!! IT DOESN’T PROOF
TRIANGLES ARE CONGRUENT!!!!
CPCTC is an abbreviation for Corresponding Parts
of Congruent Triangles are Congruent. What
CPCTC does is, it uses triangle that are already
proven congruent to proof the parts of the
triangle are congruent. You can also use CPCTC as
a justification after the proof of triangles. So the
only thing CPCTC does is proving parts of a
triangle are congruent, remember IT DOESN’T
PROOF TRIANGLES are congruent.
To have a better Idea of what I am talking about
follow these examples down below
Statement
Reason
1. AB = DC
<ABC = < DCB
Given
2.BC = CB
Reflex prop of =
3. ABC =
4. <A =<D
Prove <A = <D
DCB
SAS
CPCTC
Statement
Reason
1.EG = DF
EG DF
2. < EGD = < FDG
Given
GD =DG
Reflex prop of =
EGD = FDG
SAS
<EDG = <FGD
CPCT
ED GF
Convers of alt. int.
Alt int angles thm
Statements
1. Draw X, the midpt. of BC
2. Draw the auxiliary line AX
3.
4.
5.
6.
7.
BX
AB
AX
ABX
<B
CX
AC
AX
ACX
<C
Reasons
1. Every seg. Has a unique mdpt.
2. Through two pts. There is exactly
one line.
3. Def. of mdpt.
4. Given
5. Reflexive prop of
6. SSS steps 3,4,5
7. CPCTC
Statement
Reason
JL and HK
bisect each
other.
Given
Def of bisect
JG=LG, and
HG=KG
Vert thm
JGH=LGK
SAS
JHG=LKG
CPCTC
JHG=LKG