Question

if the diagonals of a quadrilateral divide each other proportionally then it is a trapezium​

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.

solution

Step-by-step explanation: