Corresponding Parts of Congruent Triangles are Congruent

What does CPCTC stand for?

Corresponding Parts of Congruent Triangles are Congruent

C: Corresponding
P: Parts
C: Congruent
T: Triangles
C: Congruent

Ok..but what does that mean?

It means that if two trangles are known to be congruent , then all corresponding angles/sides are also congruent.

As an example, if 2 triangles are congruent by SSS, then we also know that the angles of 2 triangles are congruent.

Practice Proofs

Practice 1

Prove KJ $$ \cong $$ JI

loading AAS proof
Practice 2

Prove ML $$ \cong $$ MN

loading AAS proof
Practice 3

The proof below uses CPCTC to prove that the diagonals of a rhombus bisect the shape's angles. This proof relies upon CPCTC.
All that is necessary for this proof is the following definition for a rhombus: a parallelogram with four congruent sides.

loading AAS proof
back toTriangle Proof