CPCTC

What is CPCTC?
CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent.

What does it mean?
It’s a fundamental theorem used in geometric proofs. It essentially states that if you have proven that two triangles are congruent, then you can conclude that all of their corresponding sides and all of their corresponding angles are also congruent (equal in measure).

The following diagram gives the definition CPCTC (Corresponding Parts of Congruent Triangles are Congruent). Scroll down the page for more examples and solutions on how to use CPCTC.

 

How is CPCTC used in proofs?
CPCTC is usually the final step in a geometric proof where your goal is to show that two specific segments or angles are congruent.

The typical flow of a proof using CPCTC is:

1. Identify two triangles in your diagram that you suspect are congruent.
   
2. Gather evidence (given information, definitions, postulates, theorems like vertical angles, reflexive property, alternate interior angles, etc.) to prove that these two triangles are congruent. You use one of the triangle congruence
   postulates/theorems to do this:
   SSS (Side-Side-Side)
   SAS (Side-Angle-Side)
   ASA (Angle-Side-Angle)
   AAS (Angle-Angle-Side)
   HL (Hypotenuse-Leg, for right triangles only)
   
3. State that the two triangles are congruent using the appropriate congruence postulate/theorem. For example, “△ABC≅△DEF by SAS."
   
4. Apply CPCTC: Once you’ve established that the triangles are congruent, you can then use CPCTC to state that any pair of their corresponding parts (sides or angles) are congruent. This is the step that allows you to prove your original goal.

Videos

CPCTC Triangle Congruence

• Show Step-by-step Solutions

CPCTC Congruent Triangles Geometry Proof
How to use CPCTC in congruent triangle geometry proofs?

• Show Step-by-step Solutions

SSS, SAS, ASA Proofs with CPCTC

• Show Step-by-step Solutions

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