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The 3D algebra problem of Shary this year

Source: Sharygin Correspondence Round 2024 P24

March 6, 2024
pyramidgeometry3D geometry

Problem Statement

Let SABCSABC be a pyramid with right angles at the vertex SS. Points A′,B′,C′A', B', C' lie on the edges SA,SB,SCSA, SB, SC respectively in such a way that the triangles ABCABC and A′B′C′A'B'C' are similar. Does this yield that the planes ABCABC and A′B′C′A'B'C' are parallel?
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