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.