(Updated 2 Jan 2013)
A quadrilateral can be dissected into a rectangle by a line joining the mid-points of one pair of opposite sides, and the perpendiculars to this line from the mid-points of the other pair of opposite sides (see http://www.geogebratube.org/student/m3459 ).
Explore how a triangle could also be dissected similarly into a rectangle, and investigate how the rectangle could become a square (the generalized Dudeney's Puzzle).
Cut Triangles into Rectangles & Dudeney's Puzzle Generalized
