Question

slove this in method...

Answer 1

heya .

I think it is converse of Thales theorm.

given-A triangle ABC and a line intersecting AB at D and AC at D.
such that AD/DB=AE/EC

to prove __DE//BC

proofe-- if possible ,let DE is not parallel to BC then ,there must be another line through D ,which is parallel to BC ,let DE//BC

then by Thales theorm we have,

AD/DB=AF/FC

But AD/DB=AE/EC(given)

from1 )and 2) we get

AF/FC=AE/EC
adding 1 on both side .


then AFFC/FC=AE/EC/EC

=Ac/Fc=Ac/EC =1/FC=1/EC

=FC=EC

this is possible only when E and F coincide

hence DE//BC.


hope it help you..
@rajukumar .

Answer 2

Hope this helps you


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