4.6 CPCTC
Learning Targets:

Understand how to use CPCTC as a reason in proofs
***********************************CPCTC*********************************************
Example 1: ∆𝑇𝐺𝐵 ≅ ∆𝐸𝐷𝐴. List all congruent
corresponding parts.
Corresponding
Parts of
Congruent
Triangles are
AFTER two triangles have been proven
congruent, we use CPCTC to prove
corresponding parts of the triangles are
congruent to each other.
Congruent
̅̅̅̅ bisects ∠𝐴𝐶𝐷 and ∠𝐴𝐵𝐷.
Example 1. Given: 𝐵𝐶
Prove: ∠𝐴 ≅ ∠𝐷
Note: We must first prove the two triangle are congruent, then use CPCTC to prove ∠𝐴 ≅ ∠𝐷.
Statement
1)
Reason
1)
2)
2)
3)
3)
4)
4)
5)
5)
6)
6)
7)
7)
A
C
B
D
Example 2: Given: ̅̅̅̅
𝐸𝐺 ≅ ̅̅̅̅
𝐷𝐹 , ̅̅̅̅
𝐸𝐺 ∥ ̅̅̅̅
𝐷𝐹
Prove: ̅̅̅̅
𝐸𝐷 ∥ ̅̅̅̅̅
𝐹𝐺.
Recall: Congruent alternate interior angles can be used to prove that lines are parallel.
E
G
D
F
Statement
1)
Reason
1)
2)
2)
3)
3)
4)
4)
5)
5)
6)
6)
7)
7)
8)
8)
9)
9)
4.6 CPCTC
Learning Targets:

Understand how to use CPCTC as a reason in proofs
***********************************CPCTC*********************************************
Example 1: ∆𝑇𝐺𝐵 ≅ ∆𝐸𝐷𝐴. List all congruent
corresponding parts.
C
P
C
AFTER two triangles have been proven
congruent, we use CPCTC to prove
corresponding parts of the triangles are
congruent to each other.
T
C
Example 1. Given: ̅̅̅̅
𝐵𝐶 bisects ∠𝐴𝐶𝐷 and ∠𝐴𝐵𝐷.
Prove: ∠𝐴 ≅ ∠𝐷
Note: We must first prove the two triangle are congruent, then use CPCTC to prove ∠𝐴 ≅ ∠𝐷.
Statement
1)
Reason
1)
2)
2)
3)
3)
4)
4)
5)
5)
6)
6)
7)
7)
A
C
B
D
Example 2: Given: ̅̅̅̅
𝐸𝐺 ≅ ̅̅̅̅
𝐷𝐹 , ̅̅̅̅
𝐸𝐺 ∥ ̅̅̅̅
𝐷𝐹
Prove: ̅̅̅̅
𝐸𝐷 ∥ ̅̅̅̅̅
𝐹𝐺.
Recall: Congruent alternate interior angles can be used to prove that lines are parallel.
E
G
D
F
Statement
1)
Reason
1)
2)
2)
3)
3)
4)
4)
5)
5)
6)
6)
7)
7)
8)
8)
9)
9)