CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." It means that once two triangles are proven to be congruent using SSS, SAS, ASA, AAS, or HL, then all corresponding sides and angles of the triangles are also congruent due to the CPCTC rule. To use CPCTC, one must first prove the triangles are congruent by one of the five congruence rules, then corresponding parts can be stated as congruent. The example demonstrates using CPCTC to prove two angles are congruent after first showing the triangles are congruent using SSS.
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4.4 CPCTC
1. CPCTC
The student is able to (I can):
? Show that corresponding parts of congruent triangles are
congruent.
2. CPCTC ¨C an abbreviation for ¡°Corresponding Parts of
Congruent Triangles are Congruent.¡±
Once we know two triangles are congruent, we then know
that all of their corresponding sides and angles are
congruent.
To use CPCTC, first prove the triangles congruent using SSS,
SAS, ASA, AAS, or HL, and then use CPCTC to state that the
other parts of the triangle are also congruent.
3. Example Given: ?LBG ? ?OGB
Prove: ?L ? ?O
1. 1. Given
2. ?LBG ? ?OGB 2. Given
3. 3. Reflex. prop. ?
4. ¦¤LBG ? ¦¤OGB 4. SAS
5. ?L ? ?O 5. CPCTC
L
B
O
G
,
BL GO
?
BL GO
?
BG GB
?
4. Example Given:
Prove: ?O ? ?R
To prove the angles congruent, we can
break this shape into two triangles, prove
the triangles congruent, and then use
CPCTC to prove the angles congruent.
R
U
O
F
,
FO FR UO UR
? ?
5. Example: Given:
Prove: ?O ? ?R
R
U
O
F
Statements Reasons
1. 1. Given
2. 2. Given
3. 3. Refl. prop. ?
4. ¦¤FOU ? ¦¤FRU 4. SSS
5. ?O ? ?R 5. CPCTC
FO FR
?
UO UR
?
UF UF
?
,
FO FR UO UR
? ?
