This document discusses the concept of CPCTC (Corresponding Parts of Congruent Triangles are Congruent). It states that once two triangles are proven to be congruent using SSS, SAS, ASA, AAS, or HL, then all corresponding parts of the triangles (sides and angles) are also congruent due to CPCTC. An example proof is provided that uses CPCTC to show two angles are congruent after establishing triangle congruence using SAS.

1. CPCTC
The student will be able to (I can):
• Show that corresponding parts of congruent triangles are
congruent.
• Use CPCTC to solve problems

2. CPCTC 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
FO FR≅ UO UR≅
StatementsStatementsStatementsStatements ReasonsReasonsReasonsReasons
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≅