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

Posted by Vimal Desai 5 years ago

CBSE > Class 09 > Mathematics

2 answers

Preeti Singh 5 years ago

It's is a right answer ?

0Thank You

Yogita Ingle 5 years 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.

2Thank You

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