Question

show that..... ABCD is a parallelogram in which the diagonal bisect each other at right angle show that it is a rhombus

Answer 1

see this attached file
then
Again
, In traingle AOB and angle COD,

OA = OC[Given]

angle AOB = angel COD [Given]

OB = OD[Given]

Traingle AOB congrant triangle COD [By SAS congruency]

AD = CB [By C.P.C.T.] ……….(ii)

Now In Traingle AOD and Triangle BOC,

OA = OC[Given]

angle AOB = angle BOC [Given]

OB = OB[Common]

angle AOB = angel COB [By SAS congruency]

AB = BC[By C.P.C.T.] ……….(iii)

From eq. (i), (ii) and (iii),

AD = BC = CD = AB

And the diagonals of quadrilateral ABCD bisect each other at right angle.

Therefore, ABCD is a rhombus

I hope this help u