Question

2. If the diagonals of a quadrilateral divide each
other proportionally, prove that it is a trapezium.
A [Board Term-1, 2011, Set-391​

Answer 1

pls see the attachment

given AO/OC = BO/OD

DRAW MO ║AB

now, AM/MD = OB/OD (By BPT THEOREM)

     But OB/OD = AO/OC

     So, AM/MD = AO/OC

      ∴OM ║ CD (converse of bpt)

       = >  AB║CD

if two sides are parallel then its a trapezium

Therefore its a trapezium