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Isosceles Trapezoid

Source: IGO 2022 Elementary P2

December 14, 2022

trapezoidgeometryparallelogramiranian geometry olympiad

Problem Statement

An isosceles trapezoid

ABCD

(AB \parallel CD)

is given. Points

E

and

F

lie on the sides

BC

and

AD

, and the points

M

and

N

lie on the segment

EF

such that

DF = BE

and

FM = NE

. Let

K

and

L

be the foot of perpendicular lines from

M

and

N

to

AB

and

CD

, respectively. Prove that

EKFL

is a parallelogram.
Proposed by Mahdi Etesamifard

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