Q:

Demonstration of a theorem in geometry

I need to demonstrate what happens when a and b>90 grades
Theorem 2.4  Been a and b angles
a) a=b if they are perpendiculars and both are acute or obtuse angles.
b) they are supplementary if they are parallels and one of them is acute and the other is obtuse.
The thing I can not visualize well is what is the meaning of the terms perpendicular and parallel in the statements.
I have this two images in the explanation:
 
Question:
Do any one has a clue where to start?

A:

The only sense I can make out of this question is that the words parallel and perpendicular are referring to the rays that form the angle.  Notice that if $\vec{AB}$ is perpendicular to $\vec{DE}$, and if $\vec{AC}$ is perpendicular to $\vec{DF}$ as in the picture, then the two angles are equal so long as they are both acute or both obtuse.
Also, if $\vec{AB}$ is parallel to $\vec{DE}$, and if $\vec{AC}$ is parallel to $\vec{DF}$ (not pictured), then the two angles are supplementary so long as one is acute and one is obtuse.

