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 https://www.geogebra.org/student/m3459 ).[br][br]In this applet, the equilateral triangle is dissected into 4 pieces by the 3 lines. [br][br]Rotate the dissections, drag the red points to get a rectangle.[br][b]CLICK [/b]any black [b]SEGMENT [/b]to show/hide its [b]LENGTH[/b]. [br][br]Drag Q to investigate its position at which the rectangle becomes a square (the Dudeney's Puzzle).

Anthony Or. GeoGebra Institute of Hong Kong.