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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