Question

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

Answer 1

Answer:

AO=CO (given)

BO=DO(given)

angle AOB=angle COD(opposite angles)

therefore tri AOB is congruent to tri DOC

therefore AB=DC

In tri AOD and BOC

BO=DO (given)

AO=CO (given)

angle BOC=Angle AOD(opposite angles)

therefore triangle BOC=triAOD

so BC=AD hence it is a trap