question_answer

ABCD is a parallelogram. If AB is produced to E such that ED bisects BC at O. Then which of the following is correct?

A)  AB = OE      

B)         AB = BE                     

C)         OE = OC        

D)         None of these   

Correct Answer: B

Solution :

In the figure, ABCD is a parallelogram where AB is produced to E such that OC = OB In\[\Delta OBE\]and\[\Delta OCD,\] \[\angle 1=\angle 2\]       (Vertically opposite angles) \[\angle 3=\angle 4\]       (Alternate angles) \[OB=OC\]        (given) \[\therefore \]\[\Delta OBE\cong \Delta OCD\](By ASA congruency) \[\Rightarrow \]BE = CD              (By CPCT) Also, AB = CD (\[\because \] ABCD is parallelogram) \[\therefore \] AB = BE