Despite the stated impossibility of constructing the trisector of an arbitrary angle, let's see what we can do by folding: Take a sheet of paper and fold an angle - like so, considering the angle to consist of the bottom edge of the paper and the crease in the paper:

Fold in half and half again like so:

Now, with the labeling shown above, simultaneouslyfold points A and B onto lines j and k, respectively. Your paper should then look like:

That's all there is to it - except that you now

1. mark the point where point A has landed by folding or making a pencil mark,

2. unfold everything, and

3. make a fold to join the left corner point A with the point where A "landed."

The points where A and B landed will be labeled A' and B', respectively, in subsequent diagrams.

Click on the diagram to simulate the folding by dragging the corner point.

Click HERE for a hint for proving that the folding process actually does trisect an angle.