So ∠ A = ∠ 2+∠ C;

Because ∠4+∠2+∠C= 180.

And because ∠3=∠4, so AD ∠ BC (internal dislocation angles are equal and two straight lines are parallel).

So ∠A+∠B= 180.

And because it has been proved that ∠ A = ∠ 2+∠ C;

So ∠ b = ∠ 4;

So AB‖DE (same angle, two straight lines are parallel)