Question

if ABCD is a parallelogram and AC and BD bisects at O so prove that ABCD is a rhombus
plzz answer this​

Answer 1

Answer:

Step-by-step explanation:

Sol:   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.