BC is parallel to angle AD because angle angle B is equal to angle D and angle C is equal to angle A
Congruent triangles are triangles with equal corresponding sides and equal corresponding sides.
Triangle ABE and triangle CDE are congruent : given
line BC is congruent to line DE : congruent side of congruent triangles
angle EAD is congruent to angle EAB : corresponding angles of congruent sides.
angle AEB is congruent angle DEC ; vertical opposite angles.
Therefore, line BC is parallel to line DE