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Poland Contests
Poland - Second Round
1998 Poland - Second Round
6
6
Part of
1998 Poland - Second Round
Problems
(1)
criterion for perpendicularity of edges AB and CD of tetrahedron ABCD
Source: Polish second round 1998 p6
1/19/2020
Prove that the edges
A
B
AB
A
B
and
C
D
CD
C
D
of a tetrahedron
A
B
C
D
ABCD
A
BC
D
are perpendicular if and only if there exists a parallelogram
C
D
P
Q
CDPQ
C
D
PQ
such that
P
A
=
P
B
=
P
D
PA = PB = PD
P
A
=
PB
=
P
D
and
Q
A
=
Q
B
=
Q
C
QA = QB = QC
Q
A
=
QB
=
QC
.
perpendicular
tetrahedron
3D geometry
geometry