We start with triangle ABC and construct a square on each side. The altitudes of the triangle extended to the opposite sides of the corresponding squares cut each square in two rectangles.
 Use the GeoGebra applet below to demonstrate Cuoco's theorem:[br][i]The pair of rectangles that share a given vertex with triangle [math]ABC[/math] have equal area.[/i][br][br]We will demonstrate this for the rectangles at vertex [math]A[/math] – rectangles [math]AMNF[/math] and [math]AEKL[/math].[br][list][br][*]Drag the slider to see the proof of the theorem.[br][/list][br][br]Drag the vertices of the triangle to see different configurations. [br][br]This applet is based on the article “[i]The Cuoco Configuration[/i]” by Roger E. Howe, The American Mathematical Monthly, Vol. 120, Dec. 2013, 916- 923.