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cutting 2 similar triangles into 2 parts, 1 similar with the starting one

Source: 2008 Oral Moscow Geometry Olympiad grades 10-11 p1

October 14, 2020
geometrysimilar trianglescut

Problem Statement

Each of two similar triangles was cut into two triangles so that one of the resulting parts of one triangle is similar to one of the parts of the other triangle. Is it true that the remaining parts are also similar?
(D. Shnol)