Question

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

Answer 1

Answer:

the angles is 360 degree

Answer 2

Answer:

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

∴ In ΔAOB and ΔAOD, we have

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.

Hope it helps.

Mark Brainer.

Thanks.

Like Follow and Rate.

Teacher.