Solution: Because ∠ A+∠ 1+∠ 2 = 180,

∠A+∠B+∠C= 180 .

So ∠ 1+∠ 2 = 180-∠ A,

∠B+∠C= 180 -∠A .

So ∠ 1+∠ 2 = ∠ B+∠ C。

Because ∠ 1=∠2, ∠ b = ∠ c.

So 2 ∠1= 2 ∠ b = 2 ∠ 2 = 2 ∠ c.

So ∠1= ∠ b.

According to the theorem "the same angle is equal and two straight lines are parallel", we can know: DE//BC.