Paper Folding Constructions Theorem:

All of the constructions of Plane Euclidean Geometry that can be performed by straightedge and compass can also be performed by folding and creasing paper. --- James R. Stuart, Modern Geometries, Second Edition

Add a hands-on component to the study of geometry...

Paper folding provides a challenging and interesting avenue for discovery which allow students to physically manipulate (play with) geometric figures. All that is needed is a flat sheet of paper. Much of the introductory work in Geometry associated with developing the basic concepts of a point, a line, and a plane, are easier to illustrate using paper folding activities.

Try This:

Show that the sum of the interior angles of a triangle add up to 180 degrees (a straight line).

First, cut a triangle from a piece of paper and mark the three vertices as shown in the figure at the right.

Second, fold the top vertex of the triangle, in this case, vertex C, so that it touches the opposite side of the triangle, side AB. Make sure that the crease in the paper is parallel to side AB.

Finally, fold the other two vertices, A and B, so that they fall on the same point where vertex C touches side AB.

Check your results...

Use a "paper ruler" that you get when you fold a piece of paper. See if the results of the three folds in the excercise above does form a straight line.