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:

given:AO/BO=CO/DO

to proove: ABCD is a trapezium

Step-by-step explanation:

proof: AO/BO=CO/DO (given)

cross multiplying,

AO/CO=BO/DO

in triangle AOB and triangle COD,

AO/CO=BO/DO (prooved above)

angleAOB=angleCOD (vertically opposite angles)

∆AOBis similar to ∆COD (SAS)

Therefore,. angleCDO= angleABO ( CPST)

But angleCDO and angleABO are alternate angles.

Hence,AB is parallel to CD and therefore,ABCD is a trapezium.

Hope it helps.