The triangle module (60 degrees)

Introduction -- Making the Modules -- Making the Polyhedra -- Jim's Origami Page
Start with a 4x3 piece of paper, and fold like an accordian into three segments:

Fold the lower left and upper right corners in. Use only the top layers. Unfold:

Valley fold along the dotted line, and unfold:

Fold the top to the diagonal line (Fold the top layer only):

Fold this new crease to the diagonal, opening as you fold:

Fold the entire module so that this newly created crease matches up with the long crease:

Unfold back to the rectangle

Remove the excess paper above and to the right of the thick lines. Note that one of these two lines does not fall on any crease lines. This can be done with inside folds or with a pair of scissors if you're willing to use scissors.

The final piece: