Explain how proving two triangles congruent can prove parts of the triangle congruent.

Firstly, you can't just say that two triangles are congruent without any given sides or angles that you can prove to be congruent. Sides and angles have to be given in order to proves that triangles are congruent. For example, you need three sides of each triangle to be congruent for the SSS (Side-Side-Side) Triangle Congruence Theorem to take place. Same for other theorems such as SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), or Hypotenuse Leg. Only proving that one of these theorems are in place can you prove two triangles, and all of its parts, to be congruent. Once you prove that the triangles are congruent using one of these theorems you can use CPCTC (Corresponding Parts of Congruent Triangles are Congruent).

*Sorry if I made this sound confusing but if you have any further questions, please feel free to ask! I'd be happy to help anytime!