Sum of Angles of Triangle equals Two Right Angles/Proof 2

Proof

 * TriangleWithLine.png

Let $\Delta ABC$ be a triangle.

Let $DAE$ be a line such that $DE \parallel BC$.

By Parallelism implies Equal Alternate Angles, $\angle DAB = \angle ABC$ and $\angle EAC = \angle ACB$.

Therefore, the sum of the three angles is $\angle ABC + \angle BCA + \angle CAB = \angle DAB + \angle BAC + \angle CAE = 180^\circ$.