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

Show that if the diagonals of quadrilateral bisect each other at right

1.	Show that if the diagonals of quadrilateral bisect each other at right angles then it is a rhombus
Answer» It\'s is a right answer ? Sol: We have a quadrilateral ABCD such that the diagonals AC and BD bisect each other at right angles at O. AO = AO\xa0[Common] OB = OD\xa0[Given that O in the mid-point of BD]\xa0∠AOB = ∠AOD [Each = 90°] ΔAOB ≌ ΔAOD\xa0[SAS criteria]\xa0Their corresponding parts are equal.AB = AD\xa0...(1)Similarly, AB = BC\xa0...(2)BC = CD ...(3)CD = AD\xa0...(4)∴ From (1), (2), (3) and (4), we have AB = BC CD = DAThus, the quadrilateral ABCD is a rhombus.