Dear All My Friends,

Please try one interesting problem: first prove following small lemma then use the lemma to prove Pythagorean theorem!

Lemma:
A, B, C are three points on one line by this order. D, E are two points on one side with respect to line contains A, B, C and AD//BE and BD//CE. F is midpoint of AC.
Result:
Area(DEF) = (Area(ABD) + Area(BCE))/2

Best regards,
Bui Quang Tuan