Extend CE through AB to f,

Because the angle AEC is the outer angle of the triangle AEF,

So angle AEC= angle A+ angle AFE,

Because angle AEC= angle A+ angle c,

So angle AFE= angle c,

So AB//CD. (Internal dislocation angles are equal and two straight lines are parallel)

Method two.

Connect alternating current.

Because angle EAC+ angle ECA+ angle AEC= 180 degrees, angle AEC= angle A+ angle c,

So angle EAC+ angle ECA+ angle A+ angle C= 180 degrees,

Namely: angle BAC+ angle ACD= 180 degrees,

So AB//CD. (The internal angles on the same side are complementary, and the two straight lines are parallel)

Method three.

Make EF//AB to the left after point e.

Then angle AEF= angle α,

Because angle AEC= angle A+ angle C and angle AEC= angle AEF+ angle CEF,

So angle C= angle CEF,

So CD//EF,

So AB//CD. (Two lines parallel to the same line are parallel)

Hope to adopt it and wish you progress in your study.