Question

ABCD is a parallelogram and e is the midpoint of a d d l parallel to B E meets AB produced at F prove that b is midpoint of a f and f b is equal to l f

Answer 1




given: ABCD is a parallelogram. E is the midpoint of AD and DL is parallel to EB. meets AB produced at F.


TPT: B is the midpoint of AF and EB = LF


proof:


in triangle ADF , 


E is the midpoint of AD and EBDF 


therefore by the converse of mid point thm.


 B is the mid point of AF.


in triangle ADF,


E and B are the mid points AD and AF respectively


by the mid point thm EB = 1/2 DF.........(1)


since EB is parallel to DL and BL is parallel to ED.


EBLD is a parallelogram .


EB =DL......(2) [opposite sides of a parallelogram are equal]


DL = 1/2 DF i.e. L is the midpoint of DF.


LF = DL = EB


therefore EB = LF


hope this helps you.