Question

11. In the figure, ABCD is a parallelogram in which
AB is produced to E so that AB = BE
(a) Prove that ED bisects BC
(b) If AD = 10 cm, find OB.
[CBSE 2012]​

Answer 1

Answer:

GIVEN-ABCD IS AN llgm

TO PROVE - 1. ED bisect BC

2. find OB

in llgm ABCD AB produced to E so that AB = BE

NOW, IN triangle BEO AND triangle DCO (LET the point of intersection be O, (BC AND ED))

1. Z BOC=Z DOC (V. O. A)
2. BE=DC
3. Z D=Z E (Aternate angles)

BY ASA rule....

BY CPCT BO = CO

SO PROVE 1. PROVED

NOW TO find OB=?

WE PROVED that OB =OC

SO AD=BC

OR AD=BO+CO or AD =2OB

10=2OB

5=OB HENCE,PROVED.