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if D and E are points on the sides AB a...

if D and E are points on the sides AB and AC of a `DeltaABC`. Such that AB=12 cm, AD=8 cm, AE=12 cm, AC= 18 cm. show that DE||BC.

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Here BD=AB-AD=12-8=4 cm
CE=AC-AE= 18-12=6 cm
Now, `(AD)/(BD)= 8/4=2cm`
and `(AE)/(EC)=12/6=2cm`
from (1) and (2) , `(AD)/(BD)= (AE)/(EC)`
DE||BC (converse of Thale's theorem) Hence proved.
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