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Prove parallelism

Source: Cono Sur 1991-problem 1

May 29, 2006

geometryparallelogramgeometry unsolved

Problem Statement

Let

A, B

and

C

be three non-collinear points and

E

(

\ne B

) an arbitrary point not in the straight line

AC

. Construct the parallelograms

ABCD

and

AECF

. Prove that

BE \parallel DF

.

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