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Byju's Answer
Standard IX
Mathematics
Congruency of Triangles
If the diagon...
Question
If the diagonals of a quadrilateral bisect each other, prove that the quadrilateral is a parallelogram.
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Solution
Given
:
A
B
C
D
is
a
quadrilateral
whose d
iagonals
bisect
each
other
.
To
prove
:
A
B
C
D
is
a
paralleogram
.
Proof
:
In
△
A
O
D
and
△
B
O
C
,
A
O
=
C
O
(
Given
)
D
O
=
O
B
(
Given
)
∠
A
O
D
=
∠
C
O
B
(
V
ertically
-
opposite
angle
s
)
So
,
△
A
O
D
≅
△
C
O
B
(
By
SAS
congruency
)
A
D
=
B
C
(
c
.
p
.
c
.
t
)
In
△
A
O
B
and
△
D
O
C
A
O
=
C
O
(
Given
)
B
O
=
O
D
(
Given
)
∠
A
O
B
=
∠
C
O
D
(
vertically
opposite
angle
)
So
,
△
A
O
B
≅
△
C
O
D
(
By
SAS
congruency
)
A
B
=
D
C
(
c
.
p
.
c
.
t
)
Since, the opposite sides of the quadrilateral are equal,
□
ABCD is a parallelogram.
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If the diagonals of a quadrilateral bisect each other, then prove that it is a parallelogram.
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