Fold a fast paper plane — and see the geometry hidden in its creases
Start with a rectangular sheet. Fold it in half lengthwise and unfold it: that first crease is a line of symmetry. Every later fold should meet the centre line in matching pairs, one on the left and one on the right.
Bring the two top corners to the centre crease. Each corner is 90°, and the fold cuts it into two 45° angles. The visible triangles on opposite sides are congruent mirror images. Repeat the same inward folds once more to sharpen the nose; the centre line is an angle bisector again.
Fold the plane in half along the centre crease, then bring each wing down. The wings are symmetric, and the angle you open between them is a dihedral angle. Change that angle and you change how air meets the wings — one reason a paper plane can climb, stall, or glide.
Pause the animation at any fold and ask the tutor why the corners line up, what angle a crease makes, or how symmetry helps the finished plane fly straight.