Question

if the diagonal of quadrilateral divide each other proportionally,then it is a​

Answer 1

Answer:

Let ABCD be a quadrilateral as shown in the above figure:

Diagonal AC and BD divide each other proportionately that is,

OC

AO

=

OD

BO

Therefore, the triangles containing these sides are equiangular that is △AOB and △COD and thus,

∠OAB=∠OCD

∠OBA=∠ODC (Alternate angles)

Therefore, DC∣∣AB

Hence, ABCD is a trapezium.