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Prove triangle areas equal (Slovenia National MO 2001 2nd Grade P3)

Source:

April 7, 2021

geometry

Problem Statement

Let

E

and

F

be points on the side

AB

of a rectangle

ABCD

such that

AE = EF

. The line through

E

perpendicular to

AB

intersects the diagonal

AC

G

, and the segments

FD

and

BG

intersect at

H

. Prove that the areas of the triangles

FBH

and

GHD

are equal.