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International Contests
Tournament Of Towns
1990 Tournament Of Towns
(270) 4
(270) 4
Part of
1990 Tournament Of Towns
Problems
(1)
TOT 270 1990 Autumn A J4 quadrs with equal sides and 2 // are #
Source:
6/8/2024
The sides
A
B
AB
A
B
,
B
C
BC
BC
,
C
D
CD
C
D
and
D
A
DA
D
A
of the quadrilateral
A
B
C
D
ABCD
A
BC
D
are respectively equal to the sides
A
′
B
′
A'B'
A
′
B
′
,
B
′
C
′
B'C'
B
′
C
′
,
C
′
D
′
C'D'
C
′
D
′
and
D
′
A
′
D'A'
D
′
A
′
of the quadrilateral
A
′
B
′
C
D
A'B'CD
A
′
B
′
C
D
' and it is known that
A
B
∥
C
D
AB \parallel CD
A
B
∥
C
D
and
B
′
C
′
∥
D
′
A
′
B'C' \parallel D'A'
B
′
C
′
∥
D
′
A
′
. Prove that both quadrilaterals are parallelograms.(V Proizvolov, Moscow)
geometry
parallelogram