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2007 Estonia Math Open Junior Contests
2
2
Part of
2007 Estonia Math Open Junior Contests
Problems
(1)
equal areas from midpoints of ABCD (2007 Estonia Open Junior 1.2)
Source:
3/27/2020
The sides
A
B
,
B
C
,
C
D
AB, BC, CD
A
B
,
BC
,
C
D
and
D
A
DA
D
A
of the convex quadrilateral
A
B
C
D
ABCD
A
BC
D
have midpoints
E
,
F
,
G
E, F, G
E
,
F
,
G
and
H
H
H
. Prove that the triangles
E
F
B
,
F
G
C
,
G
H
D
EFB, FGC, GHD
EFB
,
FGC
,
G
HD
and
H
E
A
HEA
H
E
A
can be put together into a parallelogram equal to
E
F
G
H
EFGH
EFG
H
.
equal areas
midpoints
geometry
parallelogram