plete the following proofs using the most appropriate method (SSS or SAS). en: overline(A B) cong overline(D E), overline(A B) | overline(D E), C is the midpoint of overline(A E) ve: triangle A B C cong triangle E D C STATEMENTS & & REASONS overline(B cong D E) & 1. & choose your answer... & checkmark |overline(D E) & 2. & choose your answer... & checkmark B A C cong angle D E C & 3. & choose your answer... & checkmark is the midpoint of overline(A E) overline(A C) cong overline(C E) & 4. & choose your answer... & checkmark triangle A B C cong triangle E D C & 5. & choose your answer... & checkmark

To complete the proof, we will fill in the reasons for each statement step by step.Step 1: \(\overline{AB} \cong \overline{DE}\)Reason: Given.Step 2: \(\overline{AB} \| \overline{DE}\)Reason: Given.Step 3: \(\angle BAC \cong \angle DEC\)Reason: Alternate Interior Angles are congruent when two lines are parallel and cut by a transversal (in this case, \(\overline{AC}\) is the transversal).Step 4: \(C\) is the midpoint of \(\overline{AE}\)Reason: Given.Step 5: \(\overline{AC} \cong \overline{CE}\)Reason: Definition of a midpoint (a midpoint divides a segment into two congruent segments).Step 6: \(\triangle ABC \cong \triangle EDC\)Reason: Side-Angle-Side (SAS) Postulate. We have two pairs of sides that are congruent (\(\overline{AB} \cong \overline{DE}\) and \(\overline{AC} \cong \overline{CE}\)) and the angle between them (\(\angle BAC \cong \angle DEC\)) is also congruent.Final Answer: The proof is completed using the SAS Postulate for congruence. \(\triangle ABC \cong \triangle EDC\).