Problem

Source: V.A. Yasinsky Geometry Olympiad 2017 VIII-IX advanced p4 [Ukranie]

Tags: geometry, trapezoid, trapezium, cut



In an isosceles trapezoid, one of the bases is three times larger than the other. Angle at a greater basis is equal to $45^o$. Show how to cut this trapezium into three parts and make a square with them. Justify your answer.