Another Generalization of Pythagoras's Theorem
Take any triangle ABC and construct parallelograms ABDE and CBGF that intersect with the triangle only in the sides AB and BC, respectively. Extend ED and FG to meet in H and construct a parallelogram ACKL on the third side AC such that AL and CK are equal and parallel to HB. Then the area of ACKL is the sum of the areas of ABDE and CBGF. In short: the blue area is equal to the sum of the two orange areas.