Larry Hoehn, The isosceles trapezoid and its dissecting similar triangles,
Forum Geometricorum, 12 (2012) 27--36.

Abstract.   Isosceles trapezoids are dissected into three similar triangles and rearranged to form two additional isosceles trapezoids. Moreover, triangle centers, one from each similar triangle, form the vertices of a centric triangle which has special properties. For example, the centroidal triangles are congruent to each other and have an area one-ninth of the area of the trapezoids; whereas, the circumcentric triangles are not congruent, but still have equal areas.

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