Question

the diagnols of a quadrilateral ABCD intersect each other at a point O such that  AO/BO=CO/DO. show that ABCD is a trapezium
                                                                                                                                                

Answer 1

In triangle ABO and triangle CDO AO/BO=CO/DO ( given) /_ AOB = /_COD (vertically opposite ) => AOB. SIMILAR COD ( by SAS ) => /_A= /_ C But these are alternate angles => AB || CD => ABCD IS A TRAPEZIUM