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TOT 270 1990 Autumn A J4 quadrs with equal sides and 2 // are #

Source:

June 8, 2024

geometryparallelogram

Problem Statement

The sides

AB

BC

CD

and

DA

of the quadrilateral

ABCD

are respectively equal to the sides

A'B'

B'C'

C'D'

and

D'A'

of the quadrilateral

A'B'CD

' and it is known that

AB \parallel CD

and

B'C' \parallel D'A'

. Prove that both quadrilaterals are parallelograms.
(V Proizvolov, Moscow)