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Cross's (Vecten's) theorem

First try and explain why (prove) it is true yourself. But if you get stuck, have a look at the (unedited) proof of one of my Kennesaw graduate students at Gin Chou's proof

Then explore the analogous cases below and also try to explain why (prove) why they are true. (Each one below, except the last, has a link to an article of mine on the topic).

Similar rectangles on sides of quadrilateral


Similar parallelograms on sides of quadrilateral-1


Similar parallelograms on sides of quadrilateral-2


Similar cyclic quadrilaterals on sides of quadrilateral


Continuing constructing squares on the sides

Updated by Michael de Villiers, 27 May 2010.