Question

Prove that is the diagonals of a quadrilateral bisect each other at right angle then it is a rhombus

Answer 1

Answer:

Wait I am telling u it's very long.

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.