9th Class
Mathematics
Quadrilaterals
Question Bank
Quadrilaterals
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