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Show that if the diagonals of …

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Show that if the diagonals of quadrilateral bisect each other at right angles then it is a rhombus
  • 2 answers

Preeti Singh 3 years, 4 months ago

It's is a right answer ?

Yogita Ingle 3 years, 4 months ago

Sol:   We have a quadrilateral ABCD such that the diagonals AC and BD bisect each other at right angles at O.

   AO = AO [Common]

  OB = OD [Given that O in the mid-point of BD]

 ∠AOB = ∠AOD  [Each = 90°]

   ΔAOB ≌ ΔAOD [SAS criteria]

 Their corresponding parts are equal.

AB = AD ...(1)

Similarly,  AB = BC ...(2)

BC = CD ...(3)

CD = AD ...(4)

∴ From (1), (2), (3) and (4), we have AB = BC CD = DA

Thus, the quadrilateral ABCD is a rhombus.

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