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Byju's Answer
Standard IX
Mathematics
Rhombus
Show that if ...
Question
Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
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Solution
Take quadrilateral ABCD , AC and BD are diagonals which intersect at O.
In
△
A
O
B
and
△
A
O
D
D
O
=
O
B
∣
O
is the midpoint
A
O
=
A
O
∣
Common side
∠
A
O
B
=
∠
A
O
D
∣
Right angle
So,
△
A
O
B
≅
△
A
O
D
So,
A
B
=
A
D
Similarly,
A
B
=
B
C
=
C
D
=
A
D
can be proved which means that
A
B
C
D
is a rhombus.
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