CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
CPCTC is a reasoning principle used in geometric proofs that states if two triangles are proven congruent, then all of their corresponding sides and angles are also congruent.
Key points:
CPCTC is usually applied after establishing triangle congruence through a postulate or theorem (SSS, SAS, ASA, AAS, or HL).
It allows you to conclude that specific sides or angles are congruent.
Often used as the final step in a triangle congruence proof.
Proof Example
Given AB≅DE, BC≅EF, ∠B≅∠E
Prove AC≅DF
Statements | Reasons |
|---|---|
1. AB≅DE, BC≅EF, ∠B≅∠E | 1. Given |
2. ABC≅DEF | 2. SAS |
3. AC≅DF | 3. CPCTC |
The only way we know sides AC and DF are congruent is because we know the entire triangles are congruent. This is because congruent triangles have all corresponding angles and sides congruent. This is what CPCTC is.