Some 3D Geometry

In class, we talked about this problem. I'd like you to get a feel for three dimensional geometry. Let's see if these pictures help. Work through the pictures, and answer the question at the end, "Why does this construction work?"
Given a plane and point A not on the plane, construct a line through A, perpendicular to the plane.
The givens:
A is some point not in the plane.
You can move point A as well as the other points to see what is going on in the diagram.
add a line to the plane
Now draw a line BC on the plane.
consider plane defined by A, B, C
In the plane defined by points A, B, and C, drop a perpendicular to line BC.
get one line on plane
In the reference plane, construct a line perpendicular to line BC at D.
use plane A,D,E
In plane A,D,E, construct a line perpendicular to line DE from A.
The claim is that point F is what we seek. Explain why this is the case.