MathDB
Problems
Contests
National and Regional Contests
South Africa Contests
South Africa National Olympiad
2003 South africa National Olympiad
2
2
Part of
2003 South africa National Olympiad
Problems
(1)
The diagonal of a parallelogram is trisected by...
Source: South Africa 2003
10/14/2005
Given a parallelogram
A
B
C
D
ABCD
A
BC
D
, join
A
A
A
to the midpoints
E
E
E
and
F
F
F
of the opposite sides
B
C
BC
BC
and
C
D
CD
C
D
.
A
E
AE
A
E
and
A
F
AF
A
F
intersect the diagonal
B
D
BD
B
D
in
M
M
M
and
N
N
N
. Prove that
M
M
M
and
N
N
N
divide
B
D
BD
B
D
into three equal parts.
geometry
parallelogram
ratio