Final Answer:
The statement that should be included in completing the proof is A. Corresponding Parts of Congruent Triangles are Congruent (CPCTC).
Step-by-step explanation:
In the given scenario, triangles EDB and FCE are congruent, as mentioned in the problem (EDBE - FCE). The reason we can use to prove that DB is congruent to FC is the CPCTC (Corresponding Parts of Congruent Triangles are Congruent). According to CPCTC, if two triangles are congruent, then their corresponding parts, including sides, are also congruent. Therefore, since EDB and FCE are congruent triangles, we can conclude that DB is congruent to FC.
The key to solving this problem lies in recognizing the congruence between triangles EDB and FCE, as stated in the problem (EDBE - FCE). Once we establish this congruence, we can leverage the CPCTC (Corresponding Parts of Congruent Triangles are Congruent) theorem to deduce that DB is congruent to FC.
This is because CPCTC affirms that corresponding parts of congruent triangles are congruent, and in this case, DB and FC are corresponding sides of the congruent triangles. Therefore, the inclusion of CPCTC in the proof is essential to logically and formally establish the congruence of DB and FC.
Therefore the correct answer is: A. Corresponding Parts of Congruent Triangles are Congruent (CPCTC).