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is it parallelogram? midpoints, equal segments

Source: 2008 Oral Moscow Geometry Olympiad grades 10-11 p3

October 14, 2020
geometryparallelogrammidpointsequal segments

Problem Statement

Given a quadrilateral ABCDABCD. A′,B′,C′A ', B', C' and D′D' are the midpoints of the sides BC,CB,BABC, CB, BA and ABAB, respectively. It is known that AA′=CC′AA'= CC', BB′=DD′BB'= DD'. Is it true that ABCDABCD is a parallelogram?
(M. Volchkevich)
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