show that if the diagonals of a quadrilateral bisect each other at right angles then it is a rhombus?

Asked by nandani agarwal | 29th Sep, 2010, 07:35: PM

Expert Answer:

consider quadrilateral ABCD with diagonals AC,BD bisecting at O at right angles.
so
DO=OB
AO=OC
in triangles AOD,AOB
angle AOB=angle AOD...each right angle given
AO=AO...common side
DO=OB...given
so
AD=AB.....pyth thm
similarly we can show
AB=BC
and
BC=CD
CD=AB
So all four sides are equal, hence the answer.
 

Answered by  | 29th Sep, 2010, 09:23: PM

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