Final answer:
CPCTC is used in the middle of proofs after establishing the congruence of two triangles using congruence theorems, allowing us to assert the congruence of their corresponding parts, which is necessary for subsequent steps in the proof.
Step-by-step explanation:
CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent, and it is often used within geometric proofs after two triangles have been shown to be congruent. When trianlges are proven congruent by any of the triangle congruence theorems such as SSS, SAS, ASA, AAS, or HL, CPCTC can then be applied. The application of CPCTC allows us to make further conclusions about specific parts of those congruent triangles, such as the congruence of corresponding angles or sides, which may be crucial steps in a proof before reaching the final conclusion.
In the context of the presented choices, the correct one is: C) CPCTC is used to show that corresponding parts of congruent triangles are congruent. Using CPCTC might be an intermediate step in a proof, after we have established triangle congruence but before we solve for a particular unknown or prove a needed statement in a geometric proof.