Question
Wed November 09, 2011 By:
 

In a Parellelogram ABCD, E and F are points on AB and CD such that AE=CE P.T ED ll BF

Expert Reply
Wed November 09, 2011
The question that has been asked is slightly mistyped.The correct question must beIn a Parellelogram ABCD, E and F are points on AB and CD such that AE=CF P.T ED ll BF.
Now, see in the figure below,
 
Since ABCD is a parallelogram, which means opposite sides are equal and parallel.
 
Hence, AB || CD   and   AB=CD    ....................................(1)
 
Now it is given in the question that AE = CF   ....................(2)
 
Subtract equation 2 from 1, we get
 
AB - AE = CD - CF
 
or,  BE = DF   .......................................(3)
 
Now since AB || CD this also means that  BE || DF  .................. (4)   as these are the same lines.
 
Hence from eqn 3 and 4 we get, BE || DF   &  BE=DF
 
This means that EBFD becomes a parallelogram in itself.
 
Since opposite sides of a parallelogram are parallel, hence ED || BF.
 
Thank you
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