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Contests
National and Regional Contests
Germany Contests
German National Olympiad
1965 German National Olympiad
3
3
Part of
1965 German National Olympiad
Problems
(1)
parallelogram in space, same ratio
Source: Germany 1965 p3
2/21/2020
Two parallelograms
A
B
C
D
ABCD
A
BC
D
and
A
′
B
′
C
′
D
′
A'B'C'D'
A
′
B
′
C
′
D
′
are given in space. Points
A
′
′
,
B
′
′
,
C
′
′
,
D
′
′
A'',B'',C'',D''
A
′′
,
B
′′
,
C
′′
,
D
′′
divide the segments
A
A
′
,
B
B
′
,
C
C
′
,
D
D
′
AA',BB',CC',DD'
A
A
′
,
B
B
′
,
C
C
′
,
D
D
′
in the same ratio. What can be said about the quadrilateral
A
′
′
B
′
′
C
′
′
D
′
′
A''B''C''D''
A
′′
B
′′
C
′′
D
′′
?
geometry
parallelogram
ratio
3D geometry