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

Consider triangles AOB and COD, AO = OC [Given] DC OB = OD [Given] LAOB = LCOD A AOB =: ACOD AB = CD [90° each] [SAS] Al6JB ...(i) Similarly, we can show that BC = DA Consider triangles AOB and BOC, AO = OC BO is common. and L AOB = L BOC .. A AOB =: ACOB => \AB = BC From (i), (ii) and (iii), we get AB = BC = CD = DA Hence, ABCD is a rhombus.