Question

How you could use paper folding to construct the bisector of an angle

Answer 1

This really works well with wax paper. It is transparent and it leaves a visible white line on the crease. For the perpendicular bisector of a line segment, fold the endpoints of the line segment onto each other. The crease is the perpendicular bisector. This of course also gives you the midpoint, because that is where the perpendicular bisector intersects the line segment. For an angle bisector, put the crease through the vertex of the angle and lay the sides of the angle over top of each other. The crease is the angle bisecto