What is cpctc?

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." It is a fundamental theorem in geometry used to prove that specific parts of two or more triangles are identical when the triangles themselves are congruent. Congruent triangles are triangles that have exactly the same size and shape, which means their corresponding sides and angles are equal.

The process usually involves these basic steps:

1. Prove Triangle Congruence: First, establish that the two triangles are congruent. This is typically done using one of the triangle congruence postulates or theorems such as:

   • SSS (Side-Side-Side)
   • SAS (Side-Angle-Side)
   • ASA (Angle-Side-Angle)
   • AAS (Angle-Angle-Side)
   • HL (Hypotenuse-Leg, specific to right triangles)

2. Apply CPCTC: Once the triangles are proven to be congruent, CPCTC can be applied to show that all corresponding parts (angles or sides) of these triangles are congruent.

CPCTC is a powerful tool in geometric proofs and helps in establishing the equality of sides and angles in different geometric problems.