For this problem, I will be using the equal sign instead of the congruent sign for segments.
1) AC = AB, CD = DE, m∠ABC = 70°, m∠ECB = 35° (given)
2) ∠ACB is congruent to ∠ABC (base angles theorem)
3) m∠ACB = 70° (congruent angles have equal measure)
4) m∠DCE = 35° (angle subtraction postulate)
5) ∠DCE and ∠DEC are congruent (base angles theorem)
6) m∠DEC = 35° (congruent angles have equal measure)
7) ∠DEC is congruent to ∠ECB (angles with the same measure are congruent)
8) DE is parallel to BC (if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel)