First step is the measure of segment BC is equal to the measure of segment CE. Why? Because a segment which is bisected has two parts with equal measures.
Second segment BC is congruent to segment CE. Why? Because two segments with equal measures are congruent.
Third angle ACB is congruent to angle DCE. Why? Because vertical angles are congruent.
Please look in your text for the exact wording of the theorems.
Can you finish the proof? If not I will help you further.