Question

given that in ABCD quadrileteral AC = BD diagnols bisect at right angles . we should prove that ABCD is a quadrilateral​

Answer 1

Answer:

u an find thiSol: 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.