What does C.P.C.T.C. stand for?

C.P.C.T.C. stands for "Congruent parts of corresponding triangles are congruent." This principle is fundamental in triangle congruence and states that if two triangles are proven to be congruent through various congruence criteria (such as SSS, SAS, or ASA), then their corresponding sides and angles are also congruent. This means that not only are the triangles themselves equal in shape and size, but every individual part of one triangle corresponds to an individual part of the other triangle as equal in measure.

Understanding this concept is crucial when solving problems involving triangles, as it allows for the transfer of known measurements from one triangle to the other upon establishing congruence. By applying C.P.C.T.C., you can derive necessary conclusions about side lengths and angle measures that help in geometric proofs and real-world applications involving triangles.